Revealing mistake: When Gotham City is frozen by Mr. Freeze, there is a shot of a telephone box. The icicles on the telephone box wobble as though they are made of plastic. (01:42:15)
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 Poison Ivy first enters the Turkish Bath she is wearing a green top, tights and boots but as she is redecorating just after ejecting the gang members she now has brown tights and high heels. (00:59:10)
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.
Continuity mistake: At the lab, Freeze starts to laugh hysterically and raises both arms up to his face. A shot later, they're lowered at hip level.
Continuity mistake: After the cop has his keys stolen by Ivy, check the fingers on his hand leaning on the wall: they change position depending on the shot.
Continuity mistake: Ivy takes the keys from the cop and lowers her right hand. From a different angle, it's raised.
Continuity mistake: When Ivy blows her pheromone dust at the cop, her right hand is either holding the powder container or not, depending on the shot. (01:27:11)
Continuity mistake: When Freeze freezes Frosty while he holds a newspaper, Frosty's position and the way the newspaper folds change between shots. The position and number of icicles around him also change drastically.
Continuity mistake: Ivy extends the threefold invitation to the Botanical Garden event, but a shot later, it's folded and held against her chest. (00:38:00)
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