Continuity mistake: In the scene where the postman gallops by the country house full blast and then comes back to pick up the letter from the boy's hand, you hear hoof sounds for long enough to take him hundreds of metres away, while the camera is on the boy. But when he is actually shown stopping to turn his horse around he has only come as far as the corner of the premises, maybe 20 meters away. (01:53:05 - 01:54:05)
Continuity mistake: In the beginning when The Postman is balancing on a ladder you see him holding his rifle in his left hand. When it cuts it is in his right hand. (00:03:40)
Continuity mistake: After The Postman says "Remember, the mailman is more important than the mail" he fixes his cap with his right hand. Following shot he is fixing it with his left hand. (01:51:40)
Continuity mistake: When Abby is shooting at the General, while he is hiding behind some barrels, we can see the gun holes on the barrels change between the shots. (01:29:40)
Continuity mistake: In the gas station when The Postman hears a noise, he gets up and picks up his rifle. First he's holding the rifle by its body - when it cuts, he's holding it by the trigger mechanism. (00:05:25)
Continuity mistake: For most of the time Kevin Costner has a beard, it is scraggly and grows unevenly on the sides. In one scene where he appears as the Postman early on, it is perfectly combed and there is hair where he doesn't have any naturally. I would guess they had to reshoot the scene and he was already clean shaven, so they had to "create" a beard to maintain continuity.
Continuity mistake: Towards the end of the movie, when Ford and the new mail carrier are about to be executed, the new carrier clearly takes off his hat twice to salute Ford. The first is in the long-distance shot, and when they cut to a close up he takes it off again. (02:18:10)