Big-Lipped Alligator Moment: A cop on a motorcycle drives into the TARDIS and comes out moments later to go god-knows-where while the Doctor and Grace look on.
Continuity Lock-Out: One of the problems with the film is that it included enough from the old series without properly explaining it that it wasn't going to make nearly as much sense to anyone unfamiliar with Doctor Who. Given that this was long prior to YouTube and BBC America, most Americans knew little to nothing about it, and while it tossed in all kinds of plot-points from the series it failed to give them nearly enough context. This is mentioned specifically on the movie's DVD Commentary. Sylvester McCoy and Paul McGann in particular thought that the first act of the movie should have opened up with the TARDIS landing in San Francisco (sans interior shots), thus saving the whole Bigger on the Inside thing as a big surprise for the audience during the later scene where Chang Lee steps into the TARDIS. Instead, we see the large TARDIS interior right off the bat, with no context.
Fandom Berserk Button: The movie introduces the notion that the Doctor is half-human on his mother's side. This is not something the fandom has embraced with open arms, and you'd be wise to not bring it up in discussion with them.
Fanon Discontinuity: Whether the movie is considered canon or not depends on which particular fan you talk to. However, almost everyone agrees that at the very least, the Doctor never said he was half-human (or if he did, then he was lying).
The Master: What are you waiting for? Chang Lee: The road's still blocked. The Master: This is an ambulance! Chang Lee: Oh, right. (hits the siren)
The Doctor, upon regenerating inside a morgue—specifically, in a cold chamber, while an orderly is outside watching Frankenstein. Somehow, the new, very confused Eighth Doctor kicks down the morgue door, attracting the attention of the orderly, who walks in, sees Paul McGann walk out wrapped in a sheet squinting at the heavenly light surrounding him. The orderly takes the only sensible recourse, and drops in a dead faint.
Harsher in Hindsight: Watching Eight trying on shoes and snogging Grace in the hours prior to the climax loses some of its charm value if you've seen "Fragments" from Torchwood, because you realize that it's all happening at the same time as Alex is treacherously murdering his comrades on the Cardiff team.
For one moment, the Eighth Doctor looks at a mask of Nixon intently... and then the Eleventh Doctor meets him in person in "The Impossible Astronaut".
The Master's device he plans to use to steal the Doctor's body looks suspiciously like a Chameleon Arch.
Paul McGann wore a wig in the film because he had short cropped hair at the time that was deemed inappropriate for the Doctor. His successor Christopher Eccleston had the same hairstyle and didn't have to wear a wig.
Hype Backlash: When it was announced that the film was going to receive a Blu-ray release, Whovians all over were ecstatic: this was one of the only two stories in the series's history shot entirely on film, and as such it could greatly benefit from an HD remaster. However, this excitement later turned to disappointment and even disgust when word broke out that this "remaster" was nothing more than an upscaling of the 480p broadcast tape, rather than being scanned from the original negatives.note While the movie was shot on film, all the editing (including the CGI effects) was done on 480p videotape. If a remaster was made from the original negatives, one would have to re-edit the entire product from scratch, which would be rather expensive compared to just upscaling the broadcast copy. And before you accuse the BBC being cheap, remember that that as a public-funded broadcaster they have a duty to be responsible with the revenue they receive from the license fee and they can't devote it all to Doctor Who.
The Master frequently declared that he 'wanted the Doctor's body' or something along those lines. The bondage-gear thing he put the Doctor in doesn't help. He just had that lying around, did he?
The Seventh Doctor's death on the operating table. A fairly well-done, intense scene (set to Puccini, no less!) falls apart when the Doctor gives one last ridiculous squawk agonized cry. Yes, that's what we'll call it...
Special Effects Failure: The offscreen Daleks manage to be this despite being completely unseen due to some truly awful sound design. Due to the fact that the illusion of many Daleks was created by taking a voice clip recorded at normal speed and then just speeding it up a lot to fit multiple repetitions of it into the very short scene, and the fact that they aren't even ring-modulated, they all have comically squeaky voices that sounds neither cool nor anything like Daleks.
Uncertain Audience: The creators seem to have never decided whether they were producing a jumping-on point for the general trans-Atlantic SF/"cult TV" audience, or a revival of the show for hard-core fanboys. As a result, the latter were repelled by such things as the Doctor kissing someone and being half-human and the Master being able to spit corrosive slime for no apparent reason, while the former were bemused about what this "Eye of Harmony" thing was and why the central character turned into a completely different person thirty minutes in.