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.
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.
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