Continuity mistake: In the scene where John Wayne picks up the red box of money he lifts it onto his back and walks to an open door. As he goes out the door the camera moves to outside and we see John Wayne come out of the building. Now the red box is completely on his shoulder, rather than his back.
Continuity mistake: When Jake's younger son Michael decides to show daddy his expertise with a rifle, he picks his target as "that tall tree over there, the edge of the small broken branch", and the Duke says, "Son, that's over 400 yards!" Michael says, "Nearer 500." There's no way the Duke could have seen that branch at 500 yards, because they clearly showed earlier in the movie that his eyesight was really bad. [He's long-sighted, not short sighted]
Continuity mistake: When the Duke is in the shower at the barber shop, and he shoots his shotgun through the shower door to kill the bad guy, it blows the door apart, but the bad guy doesn't even have a little blood on the front of his body after he is killed by the mighty blast.
Continuity mistake: When Michael kills the sharpshooter in the bell-tower, the man is clearly dead when he falls out of the tower, but we can hear him scream on the way down to the ground.
Continuity mistake: As James is being hassled in the bar, one of the bad guys goes through the window into the hotel room. Sam shoots him and he falls backwards through the balcony railing. The next time the railing is shown, it's put back together.