Revealing mistake: When the elephants are making fun of Dumbo in the train caboose, Dumbo's mother pulls a pin which causes the stall door above the other elephants to fall. When the door bounces back up, you can see that the animators forgot to draw the elephants' heads and trunks and only their bodies are visible.
Continuity mistake: When Lou is finally convinced that he won't get hurt being the umpire in the "Hit The Umpire" game, he runs to take his place then stops in front of the batter. As Lou runs to take his place he isn't wearing a baseball cap, nor is he holding one in his hands, but in the next shot, when he gets hit in the head by the batter, one has mysteriously appeared on his head.
Continuity mistake: When Dorothy Lamour gets out of the water and confronts Bing Crosby and Bob Hope, she's supposedly naked and covering herself with leaves. But you can see the flesh colored bathing suit she's wearing bunch up at the hips while she moves. (01:10:22)
Factual error: Abbott and Costello have inadvertently enlisted in the Army but anyone weighing 240 pounds or more will be rejected. When Costello steps on the scale, the Army physician tells him, "You're in the Army. You made it by two ounces." Medical scales at that time (1941) showed weight in whole pounds only and did not show ounces.