Continuity mistake: When Boss and Charlie are crossing the flooded main street (before rescuing the dog), Boss is holding his shotgun pointing up into the rain in one shot, then in the next shot (from a different angle), it's pointing down, then up again and so on.
Continuity mistake: Near the beginning of the movie, after the rainstorm, Charlie and Mose are digging and flopping around in the mud to get the wagon out of the hole. They are both covered in mud. As soon as they get the wagon out of the hole, Button says "Here comes Boss". As Boss rides up, Charlie is removing his gloves, which are now dry and free of mud.
Continuity mistake: Charlie's dog, Tig, is referred to once as a "she" and once as a "he". In the scene where Charlie and Boss are heading back to town to find Mose, Button indicates the dog wants to go too. Charlie refuses, saying "She's got the heart ... she ain't got the legs." Later, in the scene where Charlie buries Tig next to Mose, he says, referring to Tig, "... he was more his dog than mine."