Visible crew/equipment: In the scene when Kermit confronts Doc Hopper he comes walking out of the bar. If you look at the top of Kermit's legs when he walks out, two pair of hands can be seen moving the legs.
Continuity mistake: At the end of the scene with the ex-leper you see Brian's mother open the door to their house twice; first in the background of a wide shot, then in a closer shot. (00:15:25)
Revealing mistake: In the major helicopter scene when Ride of the Valkyries is played, the actual tape isn't going over the playing heads. (00:37:29)
Continuity mistake: In the scene where Joe Gideon is helping his daughter with dance exercises and realises that it is time to put Michelle in a cab, he carries her out of the rehearsal studio with her facing forward and her legs wrapped around his back. They turn a corner to go outside and she magically is facing him arms around his neck and legs wrapped the other way around his waist. Also Michelle suddenly grows a yellow rain jacket. There is no time lapse in the dialog which would explain this turn.
Factual error: Although it's already been mentioned that the scene of the shuttle being stolen from the back of the 747 is impossible because the shuttle wouldn't be fueled while being transported, it should also be noted that even if the shuttle was fueled, it would still be just as impossible: During the getaway, the thieves ignited the shuttle's 3 main engines to get free of the 747 and escape: the thing is, the shuttle's main engines are fueled entirely by the large external tank the shuttle and the solid fuel boosters are attached to during liftoff, and once the tank is jettisoned, these engines cannot be used. The only engines the shuttle's internal fuel feeds are the reaction control thrusters, and the Orbital Maneuvering System (which are the two smaller engines located in the bulges just above the main engines). Both the RCS thrusters and OMS engines are almost totally useless within the atmosphere, so even if the thieves managed to get the shuttle free of the 747, they could only get it as far as it would glide unpowered: In fact, they could probably get it further if it wasn't fueled. It should be noted that this is not a fictional, futuristic spacecraft: It's a bog standard shuttle, stolen from NASA, on the back of the modified 747 used by them to transport the orbiter from its landing site to Cape Canaveral.
Revealing mistake: When the sniper is shooting the cans, the close-up of the first can shows the metal peeling out as though the bullet had come from inside instead of outside.
Deliberate mistake: After having wrestled with Santini in his office, Col. Virgil Hedgepath tells Santini, "And no more assaulting corporals in the latrine." Marines use the naval term "head" in refering to the restroom, and would never call it "the latrine." However, since "latrine" is better known to civilians, this could be a deliberate mistake by the film makers.
Factual error: During the drag racing part of the film, they show an orange Plymouth lining up to race a red 57 Chevy. When the back of the Plymouth comes into view you can see a Direct Connection license plate with a Mopar logo on it. Chrysler's Direct connection line didn't exist in 1964, and the red white and blue Mopar logo wasn't around until 1972.
Continuity mistake: When the stairs are first shown, there's carpet up the middle of the stairs. At the end when they flee the house it's gone.
Continuity mistake: When Apollo Creed is approaching the ring for the rematch at the end of the film, his robe starts off done-up, next shot shows it undone and the towel around his neck loose, and then in the last shot it's back to being neat again with the robe done up. Even when he enters the ring it's all neat and tidy. (01:32:40)