They couldn't get Leonard Nimoy or DeForest Kelley to return as Spock and Bones for the opening scene, so Kirk is instead accompanied by Scotty and Chekov. As a result, Chekov seems to be acting in the capacity of a doctor when they pick up the refugees and Scotty calls Kirk "Jim".
In the alternate opening scene, Kirk boasts about his precision skydiving. Scotty 'helpfully' announces that Kirk was off by a few meters. Definitely a Spock line.
The Cast Showoff: This is the entire reason for the horseback riding scene. William Shatner is an expert at horseback riding, and having his horse walk sideways to join Stewart is pure showing off.
He even taught Patrick Stewart how to ride properly, Stewart having spent very little time on a horse (despite Capt. Picard's love of it).
Executive Meddling: Why Kirk ends up being underused and having a disappointing end. Brannon Braga (yes, him again, he always shows up in these situations) 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 crossover with TOS was actually executive producer Rick Berman's idea. Paramount had initially offered to greenlight a TNG film during the show's sixth season, Berman suggested the crossover as a "passing the baton" film, and the studio agreed.
The Merch: An extension of Playmates' Next Generation line, this all but cemented Star Trek's status as a long-runner in the toy world. Besides the figurines, there were also two new starships, one of which was a "battle-damaged" Enterprise, and the Engineering Room playset, which hooked on to the Bridge playset, and could be accessed by the sliding doors.
Real Life Writes the Plot: The Enterprise-D is destroyed and the bridge is thoroughly trashed because the models and sets were built for television and didn't have the necessary amount of detail to look good on movie screens as well as the fact that that six-foot model of the ship was an unwieldy monstrosity. The producers wanted to be able to start from scratch should they get another movie.
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".
Show Accuracy/Toy Accuracy: An example of the "both being made together" type. The action figures from the movie reflected certain aspects of the pre-production version, but did not accurately reflect the movie as released in theatres. For example, one problem was an action figure based around Captain Kirk in an orbital skydiving suit, which was from a scene which was filmed but cut from the theatrical release. Another, more famous problem with the figures was that all the Next Generation characters appear in new versions of their standard television uniforms: these new uniforms were intended to debut in the film, and were even designed by the costume department, but a last minute decision seen them pulled before filming began, replaced with the jumpsuits from Deep Space Nine (and Voyager). Nobody told the people making the action figures that these new costumes had been pulled, however, so all the action figures are wearing Starfleet uniforms that were never actually seen on screen...
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.
Troubled Production: The Paramount execs were determined to have the film released the autumn after TNG ended, resulting in an absurdly rushed schedule that started literally one week after filming on the series wrapped. Poor Ron Moore and Brannon Braga were also given an unusually short deadline to write the script, on top of numerous demands about elements that had to be put in the film. They eagerly take the opportunity to complain about this on the DVD commentary, pointing out things like how they probably could have come up with a less silly-looking way for Picard to get past Soran's force field if they'd had more time, and pointing out a blown line that was left in the final cut with Riker talking about a "big" margin of error. "If you just listen to that line, it's wrong! And nobody caught it!"
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 cast was supposed to receive newly-designed uniforms for this film, but the producers realized, after seeing early footage, that the new uniforms looked awful on screen. With no time or money to come up with new costumes, the producers settled on the cast wearing a combination of TNG and DS9 uniforms but only made new costumes for Patrick Stewart and Brent Spiner. This led to some comically ill-fitting costuming for some cast members. Jonathan Frakes wore Avery Brooks' DS9 uniform (which was obviously much too smallnote Riker's sleeves were rolled up to his elbows because, otherwise, the cuffs would only reach halfway down Jonathan Frakes' forearms) while LeVar Burton wore Colm Meaney's uniform (which was obviously much too big).
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, Spock and McCoy were supposed to accompany Kirk on the Enterprise-B. This changed when Leonard Nimoy refused to appear for what amounted to a glorified cameo, and DeForest Kelley's declining health rendered him unable to reprise his role, despite his interest in doing so. It's fairly obvious from the dialogue that it was changed little: Scotty calls Kirk "Jim," while he always referred to him as "Captain," and Chekov conscripts reporters as nurses in a no-nonsense manner.
Former TNG writer/producer Maurice Hurley wrote a competing screenplay so that Paramount could have two potential stories to use. What little is known of this screenplay would have featured Kirk time-traveling to the 24th Century. The studio ultimately went with Braga and Moore's script because it was further along.
Word of God is that the big wooden wishbone railing (where Worf had his console) was saved.
Early in development, Michael Piller (often dubbed TNG's real daddy) was approached to develop and write his own screenplay. He turned the offer down. Given his own attempt at a TNG film resulted in Star Trek: Insurrection, we may have actually dodged a bullet there.
Kirk's original death scene had Dr. Soren simply shooting him in the back. This was actually filmed, but test audiences hated it so much that it was completely reshot.