Well, there was one story element they attempted to track through the series to mixed results, and that was Bond's grief from the murder of his wife Tracy in 'On Her Majesty's Secret Service.' While an extremely effective moment in and of itself, the lingering effects of that unfortunate event make themselves known in subsequent films in fits and starts, and the Craig era of Bond would be able to handle this kind of tragedy far better in its own way. Considering this was an ongoing series with no end in sight, this method allowed anyone at any time to jump into the next movie without worrying about catching up on anything.
The behaviors that would show up from film to film, like Bond flirting with Moneypenny, were character quirks and not things that would build over the course of the series. The first in-house adaptation of the famous Ian Fleming novel, Casino Royale updates the story and setting for a post 9/11 world, and Bond himself follows suit, ditching the outlandish gadgets and. Part of the pleasure of Bond was that he received a new mission at the beginning of every film, which then saw him carry it out.
The first 20 James Bond films may have brought actors and filmmakers over from one film to another, but the plots of those films rarely carried over.
