Continuity mistake: In the final duel, when Gary Cooper is shot on his left arm, he grabs the spot where he was supposedly wounded with his right hand, then takes off the hand, and we don't see a wound and his shirt is not torn. In the following shot we see both the wound and the tear in the shirt.
Continuity mistake: After the wedding Will Kane lifts up his new wife and seats her on a sideboard. Then, after getting the kiss he asked for, he swirls her around and puts her down on the floor again. In this shot we can only see their upper bodies, but from the way the downward movement pauses while their heads are still almost at level, we can tell that she must have stepped on a stool or something before she touches the ground.
Continuity mistake: The town people are gathered in the school/church with the doors open, then they dismiss the children and close the doors. The scene cuts back and forth between the Gary Cooper and the people sitting in the pews. The children reappear with the doors open and then again gone with the doors closed.
Continuity mistake: In the final scene, after the shootout, when Kane takes off his star and flips it to the ground, the flip starts at his waist and goes out at an angle, but when the camera descends to his feet, the star is only three or four inches from his shoe. Clearly, there was a star already on the ground and the star that was flipped went much further out and out of range of the camera.