Other mistake: When Durant uses his cigar cutter to cut off Eddie's fingers, no blood is shown squirting from his severed digits and no blood is seen on the cigar cutter. (00:05:15)
Continuity mistake: Near the start, Julie sits on a sofa when discussing the bribe. In the wide shot, as she says "I wish it were that simple", she rests her left hand on her knee. It then cuts to a closeup for her next line, and her left arm is suddenly along the back of the sofa. (00:13:40)
Continuity mistake: When Peyton returns to his lab after its destruction, a burnt picture of him and Julie is on the floor. The destroyed picture shows half of Peyton's face missing. After finding a new place to stay, when the picture is put into the scanner, more of Peyton's face is visible. (00:28:10 - 00:30:40)
Continuity mistake: When Durant shows up at Darkman's hideout in a helicopter, he is holding a machine gun. In the next shot, he's holding a grenade launcher. (01:10:20)
Other mistake: At the carnival, you can see an African-American man staring at the camera for a while. I am unsure if he is a crew-member watching over the scene, or if he is just an extra trying to get onscreen.
Other mistake: Near the end, when Julie is pushed off the building by the henchmen, her handcuffs get caught on some rods that where sticking out. But this is impossible, by the way she was falling (vertically) the rods would have made contact between her legs. No way her handcuffs could have been caught like that. And they were sticking out a good foot or two from where her body was.
Plot hole: Peyton had his face burned in the explosion. In fact, he basically lost his lips, so he should not be able to talk very easily. While he could probably learn to speak normally again through other movements with his mouth and tongue, he does so too quickly to make logical sense. And his uncanny ability to almost perfectly mimic his enemies could probably be learned over time, but again is too quick to make sense.
Plot hole: Whatever happened to the one legged henchman? He was one of the villain's lead goons in the first half of the film, but he simply disappears after the scene in Chinatown. The previous correction that "Peyton didn't have time to track him down" is complete nonsense. He literally vanishes from the film. (Due to a deleted scene, but that's no excuse either way.) There's absolutely no reason he still wouldn't be in Durant's gang and in the remainder of the film.
Suggested correction: You may not agree with the filmmaker's choice, but that doesn't make it a plot hole. It's an unresolved character thread, nothing more.
It's not the filmmakers' choice, though. He was meant to be in more of the movie, but his death scene got cut by the studio to shorten the runtime. So yes, it is a plot-hole, given he was one of the main goons and simply vanishes.
This still isn't a plot hole. In the reality of the film, that character does not partake in any of the gang's activities after the last time he's seen. His presence is not integral to the plot and the story still works without his arc being resolved, so this isn't a plot hole by definition. A plot hole is a gap in the film's logic that cannot be explained, and a side character not having their story resolved on screen does not fall under that definition.
Deliberate mistake: There is just too much movement and detail in the synthetic skin masks. Peyton lost a large portion of his face in the explosion, and cannot make much expression with his own face, but somehow he can make the masks move perfectly just like a real face.
Continuity mistake: In the opening battle at the warehouse, there is frantic gunfire and battling during the scene. However, after the second car crashed, all of Eddie Black's men are suddenly dead, despite almost all of them being alive just a few seconds earlier.
Continuity mistake: When Durant fires a grenade launcher at Darkman as they are flying through the city, Durant hits a van with a clown face on it. A few seconds later Durant hits the exact same van again.
Factual error: During the scene where Peyton is hanging from the helicopter, Durant is firing at him with a grenade-launcher. He hits several cars, most of which end up in flaming wrecks. Despite this, traffic continues as normal... If you saw cars around you exploding, would you casually continue on, oblivious? This error is especially visible with the truck driver, whom reacts to Peyton landing on top of his truck, but seems oblivious to the chaos behind him.
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.
Continuity mistake: When the power goes out in Peyton's lab (when he figures out the secret of the synthetic skin), the entire lab is still filled with some light. If it was daytime, this would be believable, but it is night outside.
Continuity mistake: At the climax of the movie, in the skyscraper construction site, there is a segment where the villains are swinging large wires with metal hooks to hit Peyton. However, the number of wires swinging through the area changes during the course of the shots, and in fact, they all disappear for a period of time.
Continuity mistake: When Darkman's hand is pinned to the steel beam by the rivet there is no blood. When we see a close up of him trying to pull his hand free, there is now blood coming from the wound. When Strack calls Darkman a freak, Darkman gets angry and the blood from his hand is gone. The next shot of his hand shows blood, as he pulls it free from the rivet.
Deliberate mistake: In the climax, the villain Strack fires a nail-gun at Peyton. There are two shots where the camera is basically inside the nail looking out. In both of these shots, the nail moves straight for Peyton and then curves away at the last second, instead of moving in a straight line just past him. This was obviously done for suspense but it still is a mistake.
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.
