Continuity mistake: Just before Scorpio crashes, Avon grabs Orac and teleports to safety. When they're still aboard the ship, Orac has several wires hanging loose from underneath. When they materialize on the planet, however, all the loose wires are magically repaired and no longer hanging.
Revealing mistake: Scorpio is attacked upon entering Gauda Prime's atmosphere. The ship lurches left: everyone leans left and hangs on. The ship lurches right: everyone leans right and hangs on. The ship rolls over a full 360 degrees: no one leans or hangs on, nor do they fall out of their unbelted flight chairs. And oddly, those same chairs that held fast here tip over with ease later, when Avon escapes with Orac.
Continuity mistake: The headless android falls into a pile of rubble after an explosion, getting up with its red, white & blue striped costume in smudgy tatters. A moment later, its outfit is mended and completely clean. Still later, when the android is walking outside, its costume is dirty and shredded again.
Plot hole: Servalan & Egrorian discover their Orac is a fake when it continues to light up and make noises after the key has been removed. But this makes no sense; the key functions as it should during the demonstration. Even if it's to do with no longer being connected to the real Orac, with the shuttle getting further away it shouldn't function at all.
Plot hole: The drama on the crashing shuttle comes from the idea that a speck of Neutron material is super-heavy. Yet in the laboratory, Egrorian states that 8 Neutrons make up the core of the Tachyon Funnel. This would make it so heavy it would probably sink through the entire planet, yet Pinder, Vila & Avon wheel it about like the aluminium prop it is. And if the Neutrons are held in some sort of anti-gravity field, that would require an enormous amount of power, but Pinder uplugs it at Avon's request.