Fake Americans: In the first movie, Katie Holmes and Morgan Freeman are the only actual Americans, amid the Welsh-born Englishman Christian Bale, the English Gary Oldman and Tom Wilkinson, and the Irish Cillian Murphy (and Liam Neeson, but Ra's isn't American anyway). There are more real Americans in the second film, but the Joker is played by Australian Heath Ledger. (We can't be sure of the Joker's nationality, but he speaks with a Chicago accent).
Notably, almost the entire cast of Begins (including most of the main stars) hail from one part of the British Isles or another, although Michael Caine's character is British and Ducard is a stateless individual.
This is mostly averted in the sequels, although notably the main villains of both sequels play it straight (Heath Ledger was Australian, Tom Hardy is British and Marion Cotillard is French.)
Fan Nickname: The "Nolanverse" is a common fan-used name for the trilogy.
Fans who disliked Joseph Gordon-Levitt's character being revealed to be the Nolanverse's version of Robin have taken to calling him "Not Robin".
On a meta-level, BatBale is used when referring to the actor or the character.
The Japanese dub of both the movies and Gotham Knight had different voice casts between them (especially from Batman Begins, who had three different voice casts, depending from the network who broadcasted the movie and the DVD/BD release):
Lying Creator and Actors: The statements that Talia al'Ghul and Robin would not be in the films was supported (by lying, or simply silence) by the actors who played Talia al'Ghul and Robin.
Earlier on, Nolan also claimed that Robin would never appear in the series because Bruce Wayne himself was just starting out, and Robin "would still be a kid at this time". This one's at least true From a Certain Point of View: there's a Time Skip before Rises, and Dick Grayson—the character almost everyone assumed Nolan was referring to—is replaced by the Composite Character Robin John Blake.
Among those who auditioned for the role of Bruce Wayne/Batman? Cillian Murphy.
A video game tie-in to The Dark Knight was listed as "In Development" for several months before and after the movie came out, with Gary Oldman even discussing it in an interview with G4, but it was ultimately scrapped. The developers may have felt that releasing a video game with players beating up a recently deceased actor's digital avatar would have been in poor taste.
A large part of The Dark Knight Rises was going to be a subplot involving the Joker on trial for the crimes committed in the second film, essentially providing payoff for the "Batman and Joker fighting forever" idea set-up at the end of Dark Knight. After Ledger's death it was decided to simply cut Joker out entirely rather than recast him, since Ledger would be such a Tough Act to Follow.