Continuity mistake: In the gun store scene, first shot there are three pistols on the counter, second angle only two. (00:36:36)
Continuity mistake: Just before Russell Crowe duels with Spotted Horse, there is a rope strung across the street with what appears to be lanterns attached to it. In the next shot of Russell Crowe, the rope is gone, but Spotted Horse later accidentally shoots it down. (01:12:50)
Visible crew/equipment: When Hackman rises from the ground after the last explosion, a guy is in the upper right corner standing on a balcony holding a device with an antenna (probably a remote device for explosions). He is visible almost four seconds. (01:38:23)
Visible crew/equipment: When Herod is talking to Cort he says, "It takes a lot to scare me, I love the sensation," then it cuts to a shot facing Cort, and just as Herod turns around the moving boom mic casts a shadow on the ground, at the lower right side of the screen (next shot Herod shoots Ratsy). (01:49:10)
Continuity mistake: When Sharon Stone confronts Gene Hackman at the end, she throws the marshal star at his feet. It is an inch or two in front of his boots. After he is shot, he gets flung backwards several feet. Stone then picks the star up and throws it to Russell Crowe. She picks it up from behind Hackman's body, several feet away from where it landed but still sticking out of the sand the same way.
Other mistake: During the first round of the duels we see a part of the participants list and "Scars" is missing. He should appear between "Spotted Horse" and "Sparks" according to their order of entering the competition.
Continuity mistake: When Sharon Stone and the old man are talking in the graveyard it's raining. In the closeups, the sky is seen to be somewhat white and cloudy, but in the wide shots, the sky is a deep blue, and almost completely cloudless - and it's still raining. In the wide shot you can see the ground outside of the graveyard is bone dry.
Continuity mistake: Near the end, when Gene Hackman and Sharon Stone are finally duelling, the shadows change too fast. Before the first shots there are no shadows, then when Hackman has the little hole in his chest, there is a long one in front of him, and when Russell Crowe arrives, everything (even buildings) projects shadows over Hackman's dead body.
Continuity mistake: When Ellen flings the marshal badge towards Herod, it flies horizontally. You can even see it, still flying horizontally, on a downward curve as it starts to land. But when it hits the ground it hits vertically, so it can stick up out of the dust. It should be lying flat on the ground.
Deliberate mistake: In the scene where the characters are initially signing up for the contest, Gene Hackman's henchmen cock their weapons as they enter, then after Sharon Stone shoots the rope apart the henchmen cock their rifles again. The problem is that with a second cocking the rifles would be ejecting any chambered brass. It seems like a deliberate mistake because they cock their rifles an inordinate number of times throughout the movie; I would guess the director wanted the effect of hearing the weapons being cocked multiple times at the expense of continuity with the rifles.
Continuity mistake: When Sharon Stone blows up the building near the end, money flies everywhere. Then when she shoots Gene Hackman through the head, he flies back and falls to the ground, and there is a paper bill under his head, flapping in the wind. Later it's not there. He didn't move either.
Factual error: When Gene Hackman is shot at the end he looks down and sees the hole in his shadow. However if he was shot from someone at the same level as him, the hole would be straight, parallel to the Earth's surface. So if he could he the reasonably proportioned shadow the angle of the sun wouldn't show any hole in him at all.
Suggested correction: First, it is reasonable to assume that Hackman is significantly taller than Stone, and, given that she is firing from a hip draw the angle of entry for the fatal gunshot would be on a upward trajectory. This generally upward bullet trace combined with the evening or late day sun could be reasonably expected to cast a shadow if you suspend disbelief initially to allow that this type of wound is practically plausible.
The fact that she is shorter is irrelevant given the distance between them. For the angle of the light showing through him to make sense (and that's assuming it makes sense for it to show through him at all) she would need to be kneeling directly in front of him. The fact that, as you say, suspension of belief is required demonstrates the original mistake is valid.
Suggested correction: He doesn't see the hole in his shadow. We see him look downward slightly, then we see the shadow slightly from the side, not the view he would see. We then see him looking down at himself. It's easy to assume he is looking at his shadow, but we don't see him doing that. He could simply be staring into space, with the shadow presented for dramatic effect for the viewer.
Factual error: In the scene just before Harrod fights Ace Handlin, we see a view of Harrod's feet passing a blood stain in the dirt. This bright red color would be impossible when mixed with the dirt. Also we are led to believe that fights happen on the hour, each hour. The blood would have coagulated and been nothing but a dark spot on the ground. This has obviously been done to emphasize that the ground is bloody.
Other mistake: When Leonardo DiCaprio is shot by Gene Hackman, he lays on the ground with his feet splayed out. The bottoms of his shoes are perfectly clean, no dirt, no dust, no wear and tear. The girl that is tending to him seems to have a french manicure, or very shiny perfect nails.
Continuity mistake: Near the end of the film, Ellen tosses her father's marshal badge into the sand at Herod's right foot. In the next shot of Herod looking down at the badge, it's suddenly shifted a few inches away from his shoe.
Continuity mistake: After almost every gunfight it rains, yet there's never any mud, or even wet spots on the ground afterwards - it goes back to being as dusty as it ever was.
Continuity mistake: When Russell Crowe is in the gun shop, he has one scab on his knuckles. When he is getting ready to shoot just after, he has two.
Continuity mistake: Sharon Stone is warned at one point that the clock clicks before it chimes, the chime that tells the gunpersons to draw. The click is quite prominent in all of the times that it is used, but it only chimes after the click on a few occasions, and when it does, it's not the time indicated on the clock.
Continuity mistake: While Herod shoots the kid, the sun changes between shots.
Revealing mistake: When Herod shoots Rusty in the back before the final gunfight, a car can be seen driving down the road in the background.