The change of the Batsuit from the organic look of Batman to the armoured look of Batman Returns? Mere stylistic choice? Not so fast! In the first movie Batman is feared as being a giant bat, a literal supernatural monster. It's only when crooks get a good look at him and realize it's body armour do they realize that he's human. What helps with the illusion? The sculpted muscles on the suit. They hide nothing the armour aspect completely in favour of getting that extra fear value. But at the end of the movie Batman is publicly declared a hero and the illusion is lost. So what does he do? He scraps the "giant bat" look and dons a more mechanical and armoured looking suit, and it can be assumed with the larger plates that it offers a lot more protection.
This one is fairly obvious, but still deserves a mention. Toward the end of the film, Shreck begins shooting Catwoman after she taunts him to "finish her off", having already been killed three times (by him, the Penguin and Batman, respectively). He empties the gun on her, ending Lives #4, 5, 6 and 7, but not actually killing her. She gives him a Kiss of Death with a taser and an electric generator, frying them both. That's eight lives. At the end of the movie, we see that Catwoman is still alive. She still has one life left.
What part is supposed to be Brillaince? She outright said that right before she zaps him "Two lives left, I think I'll save one for next Christmas."
In the famous "Bruce and Selina dance" scene, just before Bruce Wayne sees Selina at the party, the music — an orchestrated version of "Super Freak" — is very much reminiscent of "Partyman" and/or "Batdance" from the previous movie. When she appears the music turns suddenly sinister and melancholic — Souxsie and the Banshees' "Face to Face", the unofficial theme song of Returns — emphasizing the difference in tone between the two movies.
I used to question why Batman wantonly kills criminals throughout the movie, but tries to stop Catwoman from doing in Schreck. Then I payed closer attention to Bruce's speech in the next movie. There, he describes the hypothetical future for Dick Grayson as killing Two-Face for revenge, but not being satisfied and killing and killing anyone to make the pain go away. Suddenly, this movie makes more sense. Batman has already played a role in killing his parents' killer (of course, this isn't getting into the theory that Jack Napier was just another victim of Bruce's projection) and can't stop because he continues to see each and every criminal as his parents' murderer. When he realizes that Catwoman is actually the woman he's been romancing, he can no longer see criminals as a faceless other onto which he can project his own issues. The real problem here is that Batman is so sidelined that you can barely see his character arc.
How did Penguin get the plans for the Batmobile? Surely that's the big plot-hole of the movie. But, hasn't it already been established that he has a knack for getting secret documents when they've been flushed into the sewer? Another possibility is that Batman had the plans hidden in public records and the Penguin found them.
The Red Triangle Gang itself is brilliant when you think about it. Who would have more reason to be afraid of clowns than the people of Gotham City?
While researching the Red Triangle Gang, Bruce learns that at the same time their freakshow included an "aquatic birdy boy" in their lineup, numerous reports of missing children would show up in whatever town the circus was visiting, implying that the Penguin has been murdering children all his life.