Continuity mistake: Jimmy comes out of his trailer in the beginning with two bags. He kicks one aside and starts to walk away. Then a few seconds later, he is carrying one bag, has some object in his other hands that we have never seen, and is wearing sunglasses he did not have on before.
Deliberate mistake: When the tribe does the ceremonial dance to bring the crow back to life, you can see the same shot of the bird leaping up twice.
Audio problem: The mine workers are chanting "Save our jobs" in the beginning, yet their mouths never match what they are saying.
Continuity mistake: When Jimmy is looking at his reflection in the toaster, in one shot, he is looking with his hands on the ground, but in the next shot, he is suddenly touching his face with his hands while looking into it.
Audio problem: Upon finding Lily's dead body, there is a wideshot of Jimmy carrying her, and he is sobbing "Oh my god. Oh my god." But his lips are not moving.
Continuity mistake: When Jimmy and Lily embrace in the beginning, their arms change position in almost every shot.
Revealing mistake: When Pestilence kicks the barrel, liquid starts shooting out, which makes no sense, as the contents are not under pressure.
Continuity mistake: Death's one thug puts baseball gear on but in the next series of shots, he goes from wearing it all, to wearing none, to wearing some of it between shots.
Continuity mistake: When Luc is kicking Jimmy at the end, in one particular shot, Jimmy is on the ground, on his stomach, but in the next shot, he is on his side.
Continuity mistake: Several of Luc's cronies have blood on their bodies/faces back at the hideout despite nothing happening to get blood on them earlier.
Continuity mistake: When Jimmy meets Pestilence at the bar, when he starts to cough, in the first shot, his whole body moves, but in the second shot, he is perfectly still, and we just hear the coughing.
Continuity mistake: When Pestilence opens the refrigerator at the dump, his cigarette goes from being in his hand to in his mouth between cuts.
Revealing mistake: When Jimmy flies out of the church, you can see his coat being pulled by a wire that was later taken out.
Continuity mistake: When Jimmy is on the bike, Lily's brother (driving the police car), who is following him, disappears in one of the shots.
Revealing mistake: During the bar-fight, the bartender flies back and hits a table, and you can blatantly see the table is a breakaway prop, because there are no screws/nails or anything holding the top on. (You can see it easily just after the top gets knocked off.).
Revealing mistake: During the bar fight, after Jimmy knocks the gun out of Pestilence's hand, he hits him with the stick-weapon, but you can tell he missed Pestilence by quite a distance.
Continuity mistake: When Lola is washing her hands, the position of her hands and head changes position between shots. In some shots her head is pointed forwards and her hands are up, in others her head is down as are her hands.
Continuity mistake: The necklaces that Luc throws onto Jimmy at the end disappear after the first few shots.
Continuity mistake: When Jimmy is talking to Lily's brother in the beginning, in one shot he is wiping dirt from his sleeve, and in the next shot, you can tell from his movement that he is no longer doing so.
Deliberate mistake: When Jimmy punches the man trying to rape Lily in the flashback, it is obvious the blow was missed, and also, such a blow would not have as much power as illustrated in the film. Nowhere near enough to knock someone back off a table onto the ground.
Answer: As I understand it, it all had to do with a spat between the director of the original Crow movie (Alex Proyas, who had "approval" of all the subsequent Crow movies) the producer of the Crow movie franchise, Jeff Most, and Miramax. Miramax eventually caved in favor of the producer and it was made into a "non-Crow entity" when Miramax reportedly signed Eminem to play the bad guy.