Plot hole: Azmael doesn't recognise the regenerated Doctor (In the shape of Colin Baker) whereas on most other occasions other Time Lords do recognize each other through telepathy. This is odd behaviour by Azmael, considering that Azmael and the Doctor HAVE actually met before, and possibly more than once. (Azmael last met the Doctor in the Doctor's fourth incarnation, and was the best teacher the Doctor ever had. On that occasion, Azmael got drunk.).
Factual error: Sharaz Jek's monitor that displays the tunnels and his androids is inaccurate. The white blobs are, as we learn later, supposed to represent his androids. He tells the Doctor that the green area is held by the army, yet on the screen the green area is populated by androids, so they could not have had control.
Revealing mistake: When Stotz cuts a hole in his ship's door, you can see that the inside of it is made of white polystyrene. They painted the outside of it but obviously forgot about the inside. Also listen to the sound it makes when Stotz punches the hole through - it sounds exactly like polystyrene.
Factual error: When the Doctor is trying to land the ship, from the video screen it appears that they are moving towards the planet way too fast to make such a safe and quick landing. Also, the ship doesn't seem to have even penetrated the planet's atmosphere yet it lands seconds later.
Continuity mistake: When the Doctor and Peri first land on Androzani, mountains are seen in the background. They disappear when Peri picks up the silica. A couple of shots later, they're back. (This mistake was mentioned on the DVD commentary; the mountain effect was left out for financial reasons).