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.
Continuity mistake: When Darkman and Durant are battling on the helicopter, Darkman drops a large hook and line from the helicopter. A few shots later, during one wide shot, the hook and line have vanished, only for them to re-appear when Darkman falls from the helicopter and catches them.
Continuity mistake: The villain fires with a nail-gun at Darkman and the nail flies for several seconds towards him. But Darkman is very close to the villain, the nail would have hit him in a tenth of a second.
Visible crew/equipment: When Darkman swings on the wire to save Julie, you can see a large wire coming out of his shirt to support his weight, and you can make out several large wires holding Julie in the shot of her being grabbed.
Continuity mistake: As Darkman attaches the hook and line (from the helicopter) to the front of the truck, in at least three different shots, the position of Darkman's entire body changes. For example in one wide shot he is crouched over, then in the next shot he is standing up, etc.
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.
Continuity mistake: When Durant and his thugs attack Peyton, as Durant asks about the memorandum, Peyton says he doesn't know what Durant is talking about. To this, Durant replies, "Unfortunate." Durant is literally right next to Peyton. Durant's thug then grabs Peyton, and it cuts to a wider angle. Durant completely vanishes between cuts. Both shots are pointed in the same general direction, so Durant should be (very) visible in the background of the wide-shot.
Continuity mistake: When Durant walks into Louis' office, after he places the glass on the table and says he's got good and bad news, his arm is either stretched out or not depending on the angle.
Continuity mistake: At Peyton's lab, after Julie tells him she can't help him and walks down the stairs, wooden crates suddenly appear on the floor between shots.
Continuity mistake: When Durant exits the courthouse the passers by are not continuous between shots. Furthermore, a woman in red reading a paper walks by twice.
Continuity mistake: When Durant is arrested, he places his right hand over his left wrist. The cop handcuffs his left wrist but, in the following shot, Durant's right hand disappears and is replaced by the cop's hand.
Continuity mistake: During the dancing freak scene, Peyton holds an iron bar and looks at his reflection on a puddle. He lets go of the bar, which falls on the floor. He then takes his hands to his head, but the reflection on the puddle shows his arms at waist level. Also, in the following shot the iron bar falls on the floor again.
Other mistake: Julie is standing 2 meters away from the building when it explodes. We see tons of glass, wood and burning debris fall everywhere, but not a single spark touches her. She remains spotless and immaculate despite the havoc.
Continuity mistake: When Durant leaves his cigar inside a beaker by a lighter, the cigar points in a 12 o'clock position. When the shot changes it's at 3 o'clock. When Peyton crawls towards it it's back to 12.
Continuity mistake: When Guzmán finds the papers at Peyton's lab he holds them by the middle. When the shot changes he is grabbing them by the corner.
Continuity mistake: At the burn ward, the doctor sticks a pin in Peyton and says "he can't even feel it." Peyton is in an 11 o'clock position moving to 12 o'clock. When the shot changes he's in a 9 o'clock position.
Continuity mistake: Peyton arrives at his destroyed lab, grabs a computer screen and holds it vertically. When the shot changes he's holding it horizontally.
Continuity mistake: At the hospital, when the doctor talks about Peyton's injuries, note that in front of him stands a group of doctors with a medicine cabinet behind them. When Peyton escapes and they all return to the room, the cabinet has been replaced by a window.
Continuity mistake: At the fair, Peyton runs away with the pink teddy elephant and Julie goes after him. She passes by a woman holding a bunch of balloons. In the following shot the woman is nowhere to be seen.
Continuity mistake: When Julie is handcuffed, hanging on some rods, in the close-up shot the watch on her right hand disappears.
Answer: It's just psychedelic imagery to try and show his fragile state of mind and how he's losing it. The shattering light-bulb is likely to show that his mind is "shattering" (as light-bulbs appearing above someone's head are often used to signify brains/ideas in fictional, particularly cartoons), and the marionette "dancing" is the first part of the recurring motif in which he sees himself as a "freak." (Which is paid off later when he starts singing a demented song about "Paying five bucks to see the dancing freak!").