Revealing mistake: After the second movie sign, when everyone gets into the theater and sits down, there's a very obvious cut, as all the characters cut immediately from the position that they sat down in to a completely different position. (00:28:05)
Visible crew/equipment: In Servo's room, Trace Beaulieu's hand is very visible operating Crow. Watch the bottom of frame when Crow approaches the Interocitor and says "Well, let's see what this baby can do." (00:48:00)
Continuity mistake: When Mike first enters the theatre, he's wearing his exercise clothes, shorts and a college t-shirt. But when the film later breaks and Mike leaves the theatre, he's wearing his blue jumpsuit.
Continuity mistake: When Crow, Servo, and Mike are using the Interoceter, Servo gets zapped in the head a few times. One of the times, there is about a two second delay from when the animated laser hits him to when his head sparkles.
Suggested correction: I watched this. It wouldn't necessarily start sparking the moment it hit him.
Visible crew/equipment: In the beginning, when Crow is digging a hole in the satellite's hull, there are several scenes where puppeteer Trace Beaulieu is visible within the hole, operating Crow.
Continuity mistake: When Mike is using the manipulator arm, Manos, to pry the Hubble loose from the Satellite of Love, he wipes sweat off his brow. This causes the arm to peel a hole in the Hubble. If the arm was matching his movements, it would have turned the hand, and not peel open the hull.
Audio problem: In the theater, there are some times when you can hear Crow speak, but his lips don't move. One instance is when Crow asks Mike, "Can I have a car like that?" Mike replies and when Crow answers back, his lips don't move for that one either.
Continuity mistake: When Mike and the Bots first contact alien Benkitnorf, he's just getting out of the shower in order to go meet his friends, so he cuts the transmission short. So why, 20 minutes later, is he still in the shower for the movie's ending?
Visible crew/equipment: During shots of the Satellite of Love orbiting Earth, it is possible to see the wires holding up the satellite on either end of the ship.