Revealing mistake: In one scene, the Penguin is making a "bat" shadow puppet on the ceiling. But there's no light behind his hands. If there's no light, there's no shadow. (01:03:45)
Revealing mistake: When the Penguin drives the Batmobile remotely, the cars it smashes are damaged just before it hits them. (01:20:50)
Revealing mistake: When The Penguin shoots the clown who says "Killing sleeping children...", as the clown falls back to the floor, you can clearly see he falls on a wrinkled, soft mat which has unsuccessfully tried to be disguised. (01:29:30)
Revealing mistake: The snow that they use floats on water in almost every scene. (00:02:00)
Revealing mistake: Outline of the broken piece Batman will yank out of the wall to save Selina is visible before he makes it. (00:15:15)
Revealing mistake: When Batman glides off the rooftop we catch a glimpse of his face as he flies over Gotham. It isn't Michael Keaton, it's a rather crude looking dummy. (01:20:15)
Revealing mistake: When The Penguin sends his penguin army out into Gotham City, the ripples/waves in the water don't match the position of some of the penguins as they swim towards the exit. (01:43:55)
Revealing mistake: After Catwoman's line "Life's a bitch. Now so am I.", she is thrown onto a diagonal roof by Batman. The roof wobbles uncontrollably as she lands on it. (01:00:30)
Revealing mistake: Catwoman breaks into the department store to blow it up. She punches her fingers through a metal access panel to get to the gas lines. Look closely at the panel - the holes are already in place at the exact locations where she punches through, they're just covered with white paint or putty. (00:55:15)
Revealing mistake: In the final scene where the Penguin's corpse is dragged in the water by the other penguins, as he's immersed in, a sort of black mat floats away from the body, which was used to make the body drag easily.
Revealing mistake: When Batman makes his first dramatic entrance to fight the clowns in his Batmobile, that clearly isn't snow being churned up by the wheels of his car.
Revealing mistake: When the Penguin is controlling Batman's batmobile, when the batmobile hits a police car a wire attached to the police car, pulling it back is visible. (01:20:20)
Revealing mistake: When Penguin is controlling Batman's car, cars he is hitting throughout the scene are seen prematurely moving out of the way before he hits them.
Revealing mistake: When The Penguin is controlling the Batmobile, in one shot Batman taps the speedometer and the whole dashboard clearly wobbles back and forth, as it were made of rubber. (01:19:55)
Revealing mistake: When the clown steals the mayors baby, he does a cartwheel down into the sewers via a manhole. As he falls down the manhole, the "brick" wall of the manhole clearly shakes as the clown jumps down. (00:33:15)
Revealing mistake: When Batman dives off the building with his bat-glider, there are two wires visible coming off his shoulders, most easily visible before he reaches the horizontal. (01:16:45)
Revealing mistake: When the clown grabs the Mayors baby, it is obviously a doll. (00:33:10)
Revealing mistake: When saving the Ice Princess, Catwoman throws a chair at Batman. The chair is clearly broken and damaged, even before it makes contact with Batman. (01:14:10)
Revealing mistake: During the climax, when a rocket hits the "Arctic World" sign and explodes, subsequently causing the polar-bear statue to fall, look closely. The scale of the fire and smoke (particularly the smoke, which looks similar to cigarette-smoke size and not the enormous plumes that such an explosion would create), in addition to the unnatural movements of the alleged large "statue" reveal that this effect was achieved with a rather obvious miniature set.
Revealing mistake: On the rooftop, Catwoman digs her claw into Batman's chest, but she clearly just puts her hand flat on his chest and you can clearly see in the first shot no claw is left embedded in his suit. (01:16:25)
Answer: It isn't. If you look at when he dies you will see that he has cuts on his face that are bleeding red. The blue liquid is more like a bile, probably similar to saliva.