Revealing mistake: When Strakk is firing the giant nail gun thing at Darkman during the climax, you can see that the gun firing does not always match the squibs going off on the beams behind Darkman.
Revealing mistake: In the grave yard scene Liam Neeson quite obviously fumbles with his American accent.
Revealing mistake: When Darkman is hanging from the helicopter above the street, dodging traffic, in one shot from the side, the camera pans to follow a car, and you can make out the shadow of a crane. This makes it very obvious that in this shot, Darkman is in fact not hanging from the copter, but rather from the crane. (This shot has been cropped to remove the shadow in some subsequent releases, but it is still visible in the original Universal DVD release).
Revealing mistake: When Peyton looses his nerve and breaks the fingers of the game operator at the fair, you can see the fake hand that was used is a very cheap prop. It looks like hollow rubber the way the skin bends in and there is no sign of muscle/bone underneath.
Revealing mistake: When Liam is in china town and holding the match under his hand, it is very obviously a prop hand used to create the effect.
Revealing mistake: When we see a shot of Peyton typing (after he makes a synthetic glove for one hand), you can see the sides of either hand fade as they move about the keyboard typing. This reveals a "split-screen" effect with a fade through the center was used to match the real hand with the animated fake hand.
Revealing mistake: When Peyton is making Paulie's mask, note the burnt right hand typing on the keyboard. It moves like a stop-motion object, revealing it's either a robotic hand or an animated effect.
Revealing mistake: When Paulie is thrown out of the window he is replaced by an obvious stuntman: His bald cap is way lighter than his skin, as opposed to Paulie's whose skin colour is homogeneous.
Revealing mistake: When Peyton's hands are about to be burnt, they are a replaced by a very obvious prop.
Suggested correction: I personally see nothing wrong with the effect. While it is indeed a stop-motion effect, it certainly doesn't look cheap, the animation of the skin burning and curling is pretty smooth, and nothing inherently gives it away outside of the fact you know they wouldn't actually burn up the actor's hands.
