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These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The James Bond theme. In an interesting choice, the familiar theme music isn't played very much in the movie... until the very last scene, when James shoots Mr. White in the leg as revenge for Vesper. So the cue to the Bond theme is not only satisfying after such a long wait, but emphasizes Bond's badass attitude. It also firmly cemented both this particular 007 and, by extension, Daniel Craig, into the role.
It also pointed out an in-story Growing the Beard, with Bond finally being ready for the rigors of his job.
Ensemble Darkhorse: Mr. White, full stop. In this film and Quantum, the character has more Crowning Moments Of Awesome in his limited screen time than the two villains of both films combined. Also, Mathis qualifies with the role as aide and confidante to Craig's Bond in this film.
Foe Yay/No Yay: What else can you say about a naked torture scene that starts off with the Big Bad Le Chiffre eyeing up Bond and saying "you've taken good care of your body"? (Well, maybe ouch...).
Harsher in Hindsight: After the embassy shoot-out, M is so angry at Bond she tells him that she's seriously considering giving him up to the authorities. In Skyfall, Raoul Silva seeks revenge on M specifically because M betrayed him to the Chinese. So that threat M made at Bond in Casino Royale is not an empty threat.
Informed Wrongness: We are supposed to believe that Bond's initially being knocked out of the tournament was due to him being arrogant and stupid. Except it was a perfectly reasonable call to make. Bond had a Kings full of Aces Full House. Literally the only two card combinations that could have beaten him were pocket aces and pocket jacks to give Le Chiffre an Ace full house, or quad Jacks. With the way the board progressed (and depending on how Le Chiffre had bet), the vast majority of poker players would think that he had a J (maybe K-J), or possibly had 10-Q to give him a straight on the flop. When the next J came out, the straight is still looking good, and if he had K-J, that gave him a full house. The king coming out on the river was NOT good for him, because if he had the straight or the J, he now has a weak hand, if he had K-J, and Bond had the other K, they are splitting the pot - hence why he would be bluffing. The probability of Le Chiffre having quads was absolutely microscopic, and yet everybody (including Bond), acted like it was a stupid and reckless call to make. It was a GREAT call to make (and Bond probably knew it since he's supposed to be the best poker player in MI6), and it was saved only by Le Chiffre having The Magic Poker EquationPlot Armor.
Older Than They Think: The idea of Bond being a humorless government-paid assassin who doesn't use gadgets and fights realistic terrorists instead of flamboyant super-criminals. Seen for the first time, this can come off as a deconstruction of the Bond mythos, but it's actually how the character was originally portrayed in Fleming's novels. Casino Royale is probably one of the most accurate adaptations of the original novels to hit the big screen.
It's also pretty much how the screen Bond was originally portrayed, in Dr. No and From Russia with Love, the first two movies of the series. In fact, the series is a whole is more cyclical on this count than anything else; it goes from grittily realistic spy thriller to progressively more over the top gadgets and villains and plots, then reboots to return back to gritty realism again. (The extremely over-the-top Moonraker being followed by the (literally) more down-to-Earth For Your Eyes Only, for instance.)
Le Chiffre: I'll feed you that which you seem not to value...
Special Effects Failure: At the beginning when Bond is tracking down the bomb maker, we see people betting on what's supposed to be a cobra fighting a mongoose. What they actually show is a cobra fighting a common domestic ferret, which other than sharing a low to the ground body type, looks almost nothing like a mongoose, is not related (or even from the same continent) and has no particular skill at fighting snakes.
Tainted by the Preview: The second Daniel Craig, a blond, was cast to a play a character that (per Fleming's description) had been black-haired for the entire franchise, all hell broke loose. A website entitled "Daniel Craig Is Not Bond" even managed to get foreign press for all the fan ranting. Also, Moneypenny and Q weren't in the movie. Then the first trailer hit. Then the movie came out. Nobody even remembers the furor anymore. Hell, Roger Moore had brown hair anyway...
The theme song becomes this on repeated viewings: It's Bond warning his future love interests about how little they'll mean to him, as he'll never be over Vesper.
Either that or M telling Bond to harden up and get the job done, if Skyfall is anything to go by.
What an Idiot: Mendel at the end. Bond is calling him and demanding to know where the money is going and who authorized it and he just keeps smiling away without any hint that he's noticed there's anything wrong. Usually you'd think something like that would be an automatic alarm that you need to stop the transaction ASAP.
Win Back the Crowd: After Pierce Brosnan's latter few films started to grate on Bond fans due to their ever-increasing silliness, Casino Royale went a long way to showing that the series was viable again, critically.
The 1954 TV film contains examples of:
It's Short, so It Sucks : It's just 54 minutes (then, again, you can see above that the other two adaptations are overly long...).