Actor-Shared Background: An anecdote by Shatner describes him fainting from exercise after chugging a beer. Whoops. He recalled the sensation of losing consciousness during Kirk's death scene. Kirk is also an equestrian, as is Shatner. Those horses were rented from Shatner himself.
Executive Meddling: Why Kirk ends up being underused and having a disappointing end. Brannon Braga and Ronald D Moore were told from the outset that a) the movie had to be a TOS/TNG crossover, b) said crossover had to be an original-cast prologue and a Kirk-cameo ending, c) there had to be a comical subplot (which is Data getting his emotion chip). The screenwriters both admitted on the DVD Commentary that despite all this, what they wrote still wasn't up to scratch (both blame being over-stretched from having to also write the Next Gen finale "All Good Things" at the same time).
The Duras sisters' attack against the Enterprise-D is essentially the same as Khan's first attack against the Enterprise from Star Trek II: The Wrath of Khan, and they're defeated the same way: the Enterprise forces their ship to lower their shields, becoming vulnerable to an attack.
Geordi gets kidnapped, tortured, and has his visor manipulated by his abductors, just like in the TNG episode "The Mind's Eye".
Throw It In: Kirk's wide-eyed "Oh, my..." just before death was improvised by Shatner. He deliberated for a while on how his character would approach death, and decided that Kirk would find it wondrous.
The concept of the Enterprise-D being destroyed and the saucer section crashing on a planet was devised in the sixth season of the show as a possible season cliffhanger. It was dismissed as being far too expensive and would require too much time to reestablish a new ship in the final season.
The original plans for the film involved the Enterprise-A fighting the Enterprise-D. Problems: a) there was no way for either crew to come out the good guy, and b) this would require budgeting, logistics, and all the other headaches for two full Enterprise crews at once. The plan was scrapped. Plus, a 23rd century Constitution-class starship vs a 24th century Galaxy-class starship would have been an utter Curb-Stomp Battle, advantage Picard.
Originally, McCoy and Spock were supposed to accompany Kirk on the Enterprise-B. It's fairly obvious from the dialogue that it was changed little once Nimoy and Kelly refused to reprise their roles for what they felt was a glorified cameo: Scotty calls Kirk "Jim," while he always referred to him as "Captain," and Chekov conscripts reporters as nurses in a no-nonsense manner.