Continuity mistake: As Batman, Robin and Batgirl are heading to the Gotham Observatory to confront Mr. Freeze in their new Bat-Vehicles, a Frostbite piloting Mr. Freeze's Freezemobile meets them, crashing into two cars blocking the Freezemobile's way. The two cars the Freezemobile crashed into are gone in a later aerial shot of the Freezemobile having its freeze ray reflected back at it by Batman's shield.
Other mistake: The two scientists that are frozen in the observatory stay frozen for more than eleven minutes, but when Batman heats them they are in perfect state.
Factual error: There are many instances in this movie where ice is doing things that ice doesn't do in the real world. Examples include Mr. Freeze freezing the pipes to make a hole in the wall, ice making things crumble all of a sudden, or something shattering easily just because a vehicle drives through something that is covered in ice.
Other mistake: Watch carefully during Freeze's opening heist: two of his goons accidentally check each other and nearly fall down. This can be seen on the left-hand side of the screen in the overhead shot (one skates next to Freeze, another skates around an ice spike) just as the camera passes a column. And where's that spotlight that follows Freeze coming from?
Plot hole: When Robin and Batgirl are defrosting the mirrors on the telescope, don't you think that at least some of the beams would reflect back at them?
Continuity mistake: Batman & Co arrive at Victor Fries' lair, and drive underneath it out of sight of the observatory on top, yet in the next scene, Victor is able to track Batman & Co's travel with the magnifying glass, which is impossible as they are already underneath he lair.
Audio problem: When Mr. Freeze talks about his plan to freeze the city, he yells out "It'll be winter forever here in Gotham," but if you watch, his mouth doesn't match his voice at all through the entire sentence.
Revealing mistake: After Batman slides and kicks Freeze, there's a protruding lump under his clothes where the safety cable holding him was.
Revealing mistake: At the diamond gala, Batman several times punches a few henchmen of Freeze, but doesn't even touch them at all.
Plot hole: After Freeze blasts Robin with his cold ray he just picks the diamond out of his hand with no problem. Why didn't the diamond freeze along with Robin?
Factual error: If everyone had been frozen for that length of time, their blood would crystallise, which would kill them. I imagine some of the buildings and anything made of glass might crack as well, but I don't really know about that.
Continuity mistake: When Bat Girl and Poison Ivy are fighting by the lily pad pond nowhere can you see Robin who is still supposedly fighting the vines underneath it.
Revealing mistake: When Batman is snagged by Poison Ivy's vines and pulled up to the ceiling, you can see that the sides of his cape are attached to his thighs by black strings, to keep his cape from falling completely down over his head during the shot.
Revealing mistake: In one scene where our heroes are defrosting Gotham city using the sunlight, we see Commissioner Gordon stepping from his car which has been covered in flexible icicles.
Continuity mistake: When Bruce and Julie go to the party in the observatory and are swamped by people, in the overhead shot at the start of the scene we can see that Gossip Gerty is trying to get to Bruce and Julie and that there is a man between Gerty and Julie. However, in the next shot (a tighter shot of the couple and onlookers), Gerty is suddenly right next to Julie, in the place where the man had been, with no time for him to move.
Character mistake: Julie Madison, when having dinner with Bruce Wayne, says that he just called her Ivy. He didn't, and never does in that scene.
Deliberate mistake: During the opening battle scene, Mr. Freeze's gun gets stuck on top of a statue. Mr. Freeze then throws a chubby security guard up straight up into the air to knock his gun down. But it's completely wrong and defies the laws of physics. The security guard bumps the gun from the front, causing it to fall FORWARD and STRAIGHT DOWN, when in reality, the angle from which the guard smacked it in the front should have knocked the gun backwards even more. This reveals that the gun was just pulled down by a wire or was pushed forward from behind, as it completely defies the laws of physics and action/reaction.
Continuity mistake: In the last fight against Bane, Bane has got Robin and Batgirl by their throats against an icy wall. In a close-up of Batgirl, Batgirl's right hand is near Bane's spiked wrist guard. However, in the very next shot, her right hand is more near Bane's elbow.
Chosen answer: Purely a creative decision, but based on the tone of this question I don't suppose you're honestly after an answer so much as you are just looking for someplace to express your distaste.
Phixius ★
Because Schumacher wanted to base the suits on Greek sculptures hence the nipples. Don't forget Robin's shorts or Batman wearing different colored cowls in the comics, perhaps this was a nod to that.
Rob245