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Continuity: 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.
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: 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.
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.
Continuity: 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.