Revealing mistake: In the scene where Cobb's mean attack Emmitt, Mal shoots one of the men in the hand. The shot pauses long enough to show that hand is quite a cheap, plastic-looking fake prop hand.
Continuity mistake: In the gunfight scene in the street between Paden and Cobb the length and angle of the shadows of both characters and the buildings change several times from one shot to the next.
Continuity mistake: When Paden and Emmett are camped out you see Emmett pour himself a cup of coffee and he's holding the cup in his hand. The camera angle changes to a shot from behind him and you see him reaching down to pick up his cup of coffee.
Continuity mistake: In Westerns, it is common to use several horses in place of one. However, after Kevin Kline makes a huge fuss over his bay mare, they used four different horses with distinctly different markings throughout the movie. They did a better job of matching Kevin Costner's horse although a pinto is a more difficult colour to match. Also, in one scene, Danny Glover's horse changes from a sorrel (red) to a bay (brown).
Continuity mistake: When Paden finds his horse he is unarmed, so he purchases a gun and runs into the street to confront the thief. The thief fires at Paden, and while Paden is loading his new revolver one of the thief's' shots blows a hole in the back of Paden's drawers. In the next shot we see Paden's reaction as he looks at the crotch of his drawers and there is no bullet hole in the front of them.
Other mistake: When Jakes shoots the two men on the porch of the saloon at the same time, he never aims high enough to hit either of them in the chest, as shown. At best, he would have hit them in the knee but no higher.
Other mistake: When Jake gets his horse back during the shootout at McKendrick's ranch, McKendrick's men have the horse in a stall in a barn unsaddled but still wearing a bit, bridle and reins. With a bit in its mouth a horse can't eat or drink naturally, and anyone who knew anything about horses would never stall one while it was still wearing them.
Continuity mistake: Throughout the film, Emmet is depicted as being left handed. At the end, when McKendrick shoots him in the leg, Emmet is shown with the reins in his right hand and gun in his left. But when McKendrick's shot hits him, Emmet is shown dropping the gun from his right hand. As the gun hits the ground, Emmet is shown with the reins in his right hand again.
Other mistake: In the gunshot scene at the McKendrick's, a man with a sling on his arm is shot in the chest. He raises the arm, and though some blood can be seen on the sling, there is no blood or even a bullet hole on his chest. (01:48:15)
Plot hole: No one hears the gunshot in the jail. The townspeople would come to see where the shot was fired. (01:39:28 - 01:39:52)
Answer: I first saw this film in a theater, and later on DVD and TV, and I don't recall the scene you described. If his hand had been injured that way, the injury would have lasted throughout the entire film and that was not the case. Perhaps you're confusing this with another movie.