Revealing mistake: Scorpio is in stationary orbit over the planet Malodaar - but a shaky special effects matte causes the "stationary" ship to wiggle and wobble severely. (00:00:45)
Factual error: Maybe they took time in the midst of a desperate escape to tack Orac down with Velcro? When the shuttle first takes off, its angle of ascent causes Orac to nearly slide off the control panel. A short time later, the angle is far steeper, but this time Orac stays perfectly still. (00:36:15 - 00:44:55)
Character mistake: Whilst brutalising Pinder, Egrorian asks if he can feel his humerus grinding against his radius, but the bones in the forearm are the radius & ulna. The humerus is the single bone from the shoulder to the elbow.
Audio problem: Just before Avon reveals Orac is on the shuttle, you can hear his operating noise. If we can hear it, so should Vila.
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.
Suggested correction: Neutrons and Neutron material do weigh differently. 8 neutrons would weigh 8 atomic mass units - immeasurably small. Neutron Material on the other hand is comprised upon trillions upon trillions of neutrons compressed by gravity into a very small volume (and is the theory behind black hole formation). A microscopic fragment of Neutron Material would indeed have a very very large mass, but too massive even for Avon to move. That and the fact that Neutron Material comes from a Neutron Star raises the question of how it was extracted, cooled and moulded into a lump of perspex.