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.
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.
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)
Audio problem: Ivy tells Robin that Freeze wants to turn Gotham into "an ice cube" but she's not mouthing those words. (01:38:14)
Continuity mistake: During the press conference, Julie's hand swaps from being lowered to brushing her hair between shots. (00:35:57)
Audio problem: When the telescope is falling and the two people are with Batman, he tells them to grab onto his belt. The audio is terribly clipped.
Continuity mistake: While Bane is driving the limo, after Ivy puts on the wig, the gloves on her hands disappear.
Revealing mistake: At the gala, you can notice the stunt double driving the ice truck for Arnie.
Revealing mistake: In the museum, when Robin breaks the door with his bike you can notice that the door is made of foam rubber or similar.
Revealing mistake: When Batman is about to defrost Robin, he is holding a dummy.
Revealing mistake: While Ivy is fighting Batgirl you can see the stunt double replacing Uma Thurman.
Continuity mistake: Bane is pulling Robin and Batgirl but in the next shot he's pushing them.
Revealing mistake: When Batman is doing his little sliding stunt on the dinosaur exhibit when he and Freeze meet at the beginning, it's obvious that he has roller skates on and is on a rail. (00:05:10)
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