I love Casino Royale. I think it's easily the best Craig Bond film, one of the best Bond films ever, and one of my favourite films in general. It's got everything you want, and the cast is terrific. The plot, however, is interesting.
So the first watch through, my thoughts go like this: Vesper slowls falls for Bond, Mathis betrays Bond and Vesper, Vesper makes a deal while being tortured in exchange for Bond's life, they are freed, Vesper falls for Bond, they escape, Vesper sees her contacts and has to make good on the deal. But further watchings make it seems more than that.
Vesper's sudden affection for Bond, is that mostly an act? She clearly likes him somewhat, but it would seem that she is acting most of it. It is interesting how (in the scene with Bond in a chair) she is sexually aggressive on him, but after some honest words from Bond she is moved and cries a bit. As in, that's the honest side of her.
It would mean that she is pursuing Bond to get access to the money to transfer it to Quantum. Which makes sense... right? Or does it?
Because: She is putting in the routing number for the funds. Bond puts in the password he picked, but it does not seem Vesper has to put in the routing number for the MI6 account. So what is all that for? Why couldn't she just have put in the Quantum tracking number and left?
Which makes it more confusing. If Vesper is a double agent the whole time, why is LeChiffre there? Is Vesper working higher up the ladder than LeChiffre? Why would they care who wins if it is down to Bond and LeChiffre? Vesper would just transfer over the money.
Which is FURTHER confusing because why wouldn't Vesper restake Bond? It would seem that would be the best way to ensure one of the two wins.

But let's assume Vesper has to put it into an account made for the tournament, and they are to transfer it from that account to MI6. And that she has to win over Bond, keep him from returning to transfer the money, get to a drop off city, then make the drop off. That whole sideplot should check out, minus why Quantum wasn't leveraging Vesper the whole time. Let's move on to a nice wrinkle added by QoS: How is Mathis NOT a double agent?
Seriously, the entire structure of Casino Royale is ruined if Mathis is not a double agent. There's no way Vesper was in on this all herself. It would add all of the problems listed above, plus the whole problem of why LeChiffre mentions Mathis by name. (Personally I would have made Mathis the villain of the third film, as I thought it was terrible to bring him back, then even worse to kill him off instantly. I loved his sidekick character and thought he'd have been a great addition to the franchise as it was going. They basically had a Mathis in Skyfall anyway. Grrr Skyfall.)
Casino Royale's plot just needs a little tightening I think. Vesper having a previous connection to Quantum isn't as good as Vesper making a deal with them as it happens. And I don't know what Mr. White meant to LeChiffre saying "know who to trust". It comes off a little as "We don't have a plot in mind but this is vauge but sounds meaningful."
Still love the film. Wish the rest of the series had followed in its footsteps with a strong female lead with dynamite chemistry with Craig and lots of Bond in civilian locations being suave. But I'll always have it, and I'm very grateful for that.

I realize this is long AF, but bear with me!
So, one of the major complaints I've heard from critic reviews, the discussion threads on Reddit, and from some friends I went to see Spectre with are that Spectre went too far in the direction of the old Bond movies and that the tone/plot of the movie were too far removed from the previous Daniel Craig outings.
I would like to offer my two cents and contend that Spectre is the end result of a very gradual, skillful evolution of the rebooted Bond and to maybe patch up some of the perceived plot holes that came from retconning Blofeld as the "author of all [Bond's] pain."
INITIAL DISCLAIMER: I liked Spectre, but do not think it was as good as either Casino Royale of Skyfall. It's definitely better than Quantum of Solace. I'd give CR a 9/10, Quantum a 5/10, Skyfall a 9.5/10, and Spectre a solid 7/10... maybe a 7.5 if you forgive some of the lackluster London scenes and the sorta slow editing.
So, to begin: Craig's Bond has been evolving each film.
I've heard a lot of people say they were very disappointed in how Bond went from the heartless bastard who will never love again to a guy willing to throw it all away for one girl... again. Let me show how I feel Craig's Bond has been evolving to this point, a point similar to how Connery's Bond was the second we first saw him in Dr. No.
In CR, Bond is young, reckless, and doesn't care who gets hurt. After Vesper breaks his heart, he becomes hardened, callous, and vengeful. If you think about it, because Quantum is a back-to-back sequel with CR, both of those films take place in 2006. If Skyfall takes place in 2012, that means Bond had SIX YEARS to evolve and change. We know at the end of Quantum that he has forgiven Vesper and healed from the trauma she caused him. And then, if we see that Spectre takes place in 2015, THREE YEARS after Skyfall, that means NINE YEARS TOTAL have passed since Bond lost Vesper. I think that, when we think of Craig's Bond in these terms, we see that he has had plenty of time for his heart to soften again and be open to falling for the next right woman, who so happens to be Dr. Madeleine Swann in Spectre.
For proof of Bond's softening heart, let's think of M's death scene in Skyfall. We see a Bond here that openly weeps for a friend. This woman could have just been his boss. He could have had a multitude of reactions to hear death: "Oh, shit, I basically killed my boss by not protecting her and leading her out to the country, I'm in big trouble." But instead, he weeps, and we see that Bond has let this woman in his heart. She was his friend, his mother-figure, and the Bond girl that might have touched him just as much as Vesper Lynd.
Further softening is evidenced in Spectre. Bond seduces Monica Belucci's character, sure. But notice that he gets the information he wants from her before any lovemaking happens. And Bond could get sex anywhere he wants, it's not like he's starving for a good hump. I contend, as awful as this might sound, that Bond, in his own way, was comforting her with the sex scene. He doesn't have to do this AT ALL, but he provides her with some much needed physical attention in the wake of her grief and emotional distress. In addition, he leaves her Felix Leiter's number and provides her a way out of the dangerous situation she's in, something else he is not obligated to do by any means. He's making two very conscious decisions here to be a good, caring guy (by Bond-universe terms).
Let's think back to CR... In that movie, Bond nearly sleeps with Demitrious's wife in order to learn more about him and his connection to the terrorist organization Le Chiffre is in charge of. The second Bond gets the information he needs (that Demitrious is going to Miami), Bond leaves her flat, knowing she's vulnerable and in danger. When M shows him her dead body, Bond is completely cold and fine with it. He has no remorse. Just from the difference in these two widow seductions, and from his deep relationship with M, we see that Bond has evolved a whole heck of a lot between CR and Spectre. After 9 years and a whole lot of growth, it seems completely logical to me that he could be ready to fall in love again.
Next up is reconciling the retconned SPECTRE with the various villains in the previous Craig Bond flicks. I believe this can be done by categorizing the previous villains as either loose cannons that Blofeld left free to wreak havoc on Bond or villains that were actual SPECTRE members.
Silva is the most obvious loose cannon. None of this is explained in the films, obviously, but this speculation of mine makes sense to me, and maybe it will help the whole "I was there the whole time" reveal go down easier for you guys. Let's picture Silva after M gives him to the Chinese in exchange for 6 other British agents the Chinese were holding. Silva is delirious, tortured daily, and completely vengeful against M, the woman responsible for this ill treatment. Imagine if, at this opportune moment, Blofeld or a SPECTRE agent steps in and frees him. Either that, or Silva escapes on his own and is later offered money and equipment from Blofeld/SPECTRE to set up his own operations. Blofeld wouldn't be interested in employing Silva as an actual SPECTRE member, he just wants to help out anyone who will wreak havoc on MI6. Perhaps SPECTRE even offers some of the jobs Silva mentions to Bond that he is working on: dismantling governments and assassinating dictators. Now, of course Blofeld later takes direct credit for Silva's killing M (which is funny because M is injured by a chance gunshot from one of Silva's henchman... not exactly a deliberate blow from Silva). I don't think we have to accept that as story truth. It's most likely just a lie that Blofeld tells Bond to push on his buttons. (We do know that Silva IS directly linked to Blofeld/SPECTRE through the ring Bond finds early on in the film.)
Le Chiffre, then, would be another rogue agent loosely employed by SPECTRE. The little "I want to make a bank for terrorists" scheme almost sounds like an outside proposition that Le Chiffre would bring to SPECTRE through Mr. White, who we see all throughout CR and Quantum. I would contend that Le Chiffre was never a direct SPECTRE member or even really working for them. He was just a guy they saw useful to employ... Until his little scheme didn't work, upon which Mr. White dealt with him for SPECTRE ("Money isn't as important to my people as knowing who to trust.")
The other subset of previous Craig villains would be those who ARE directly employed by SPECTRE, or are even full members/partners in the organization.
I contend that Quantum, which everyone thought was the thrift shop excuse for SPECTRE the writers wanted to employ for Craig's Bond, is actually the name of an OPERATION/EVIL PLAN, not an organization. Think about it: Mr. White mentions "His people" and "We," but never actually calls them Quantum. The only person who name drops "Quantum" is Greene, and the line he says is "I've told you everything you wanted to know about Quantum." He doesn't confirm that Quantum is the organization he's a part of at all. I think it makes sense, what with the retconned SPECTRE and all, to think of Quantum as the name of the plan SPECTRE put Dominic Greene in charge of operating, which allows Quantum of Solace and Spectre to co-exist quite nicely.
I would also claim that Greene is a direct SPECTRE member due to that scene where all the baddies talk to each other with ear pieces during the performance of Tosca. Mr. White is shown clearly in this scene as well, which makes sense given that White is explained to have been a direct member of SPECTRE in Spectre. We don't see Blofeld in this scene simply because a) Blofeld might not want to show up for a simple meeting like this when he can leave it to Greene or b) Blofeld follows his trend of not speaking in meetings unless he must ("Please, don't let me interrupt" upon his entrance in Spectre). Later on when Bond crashes the party, all the members including Greene leave the opera post-haste, while Mr. White stays right where he is, not drawing attention to himself. I would contend that, if we accept the story truth that Blofeld was at this SPECTRE meeting, he would have been smart as well and would have stayed put.
For further thought, consider "Ellipsis" in Casino Royale. In this film, the evil plot/password/catchphrase of the terrorist organization Le Chiffre operates is Ellipsis. It's the name of one of the contacts on Madagascar Bomb Maker's phone, it's the password T-1000 guy uses at the Miami airport, and it's the go-word used by Le Chiffre to start the operation. However, we never make the assumption that, say, Le Chiffre's organization is called Ellipsis. I would argue that the word "Quantum" is used much the same way in Quantum of Solace.
Finally, I get to the idea that the filmmakers and Craig's Bond have gone through a whole lot of crap and emotional trauma to EARN what Spectre is, which is basically a good-old traditional Bond flick. This is the Bond of your grandpa, the Bond who is already set in his ways and knows the ropes of the spy game. What people loved so much about CR, Quantum, and Skyfall was that we saw what you could call "Bond Begins," or the events and backstory that shape Bond, backstory we never got to see before. The only problem is that you can't keep Bond an immature Bond forever. At some point he has to be the full blown, full grown Bond we all know from folks like Sean Connery, Roger Moore, and Pierce Brosnan. I think three movies, 7 hours or so of screen time, and 9 years of story time are more than enough to get Bond to the point he is at in Spectre.
And, if you think back to the ending of Skyall, Mendes and team were directly setting us up for Spectre. We see the female M pass and make way for the traditional male M (a move that, surprisingly, doesn't get hate for being backwards or old-fashioned, but is seen as a move towards Bond tradition.) We see Eve retire from the field and become a secretary, Ms. Moneypenny, another move that didn't have the feminist crowd up in arms because a) I would venture to guess that not a lot of feminists watch Bond flicks and b) this decision is once again a way to bring us back to the Bond we saw in the days of Connery and Moore. We get our traditional Q, though certainly revamped for the modern day. And finally, we even get the traditional, leather-door office for M(allory) to conduct MI6 operations and give Bond his assignments.
In short, we have had three movies to set up Bond full stride, Bond in his prime, Bond as he was performed by Connery before. If we think of the three previous movies as an evolution leading up to Spectre, the fantastical, '60s Bond throwback, almost-but-never-exactly campy tone of Spectre makes a whole lot more sense.
TL;DR: Spectre makes sense and fits in with the previous Craig Bond films because Bond as a character has had 9 story years to evolve and change, because Silva and Le Chiffre could have been loose cannons while Greene was an actual employee of SPECTRE, and because we had three "Bond Begins" movies to get us to this point in the series.