Character mistake: After Maverick gives the "actors" their hundred dollars, he says "News travels fast in the Old West." Why would he refer to the west as "old" when, for him, it's the present? This is an expression that didn't come about till later on, when the west BECAME old.
Continuity mistake: When we see Maverick for the first time in the hanging scene he is sitting on a horse with a rope around his neck, which is completely covered by his collar. When the camera angle changes the knot is much higher and the rope is fully visible, although the horse hasn't moved yet. (00:01:35)
Continuity mistake: The smudge that Maverick gets on his collar in the subsequent fight changes shape from when he's outside to when he's inside. (00:16:50)
Continuity mistake: In long shots of the town when the movie begins, the town is on different banks of the river in different shots.
Revealing mistake: During the explanation of security procedures on the paddlewheeler there is a modern ceiling fan in the backround. (01:21:00)