Other mistake: As Dark Helmet says his line "Everybody knows that!", watch the crewman in white to Helmet's right. He starts to cover his crotch a beat too soon.
Revealing mistake: In one of the shots of Dot in the "Mercedes" near the beginning, the outline of the blue screen is visible around her.
Continuity mistake: After Lone Star and Barf drop the giant hair dryer, they lift up the empty case. In the "Instant video Cassette" of the movie, Lone Star and Barf are lifting the case, but the hair dryer is missing.
Suggested correction: It's not the same scene. Notice that in the scene where they drop it, it's relatively flat where they are walking. In the instant cassette scene, they are walking down a hill.
They were by a hill, but the angle didn't allow the camera to see it.
Revealing mistake: As the ship goes to Ludicrous Speed, Dark Helmet goes horizontal, and as he does, you can make out of the wires pulling on the bottom of his cape.
Visible crew/equipment: In the desert, Helmet asks the guys "combing" the desert if they've found anything. The camera crew is reflected in the helmet of the guy that says "we ain't found shit."
Revealing mistake: When Vespa starts shooting at the guards on the platform, the one on the end flips over when shot, and you can see him bend over after he's shot to prepare himself for the stunt.