Continuity mistake: When Sarah falls from the scaffolding, a plank of wood saves her from death. Trouble is, she fell a foot from the outside of the scaffolding and most of the plank was inside the scaffolding, therefore her feet would have hit it and she could only have landed with her head pointing inwards. But when we see her, her head is pointing outwards.
Revealing mistake: During the Doctor's early conversation with the Time Lord, there is fog swirling around them. When the Doctor agrees to take on the mission, it suddenly appears very concentrated around the tip of the rocks behind them, as if generated from a source behind the rocks. Normal fog would not do this, and it's clear that dry ice was used as the fog effect (DVD commentary confirms this).
Revealing mistake: Whenever there's a close-up of Davros, it's very easy to see that there's a gap around his mouth where the mask should blend in with the actor's face, but doesn't. This mistake was rectified, incidentally, in Davros' next appearance in "Destiny of the Daleks."
Continuity mistake: At the very beginning, Sarah comments to the Doctor that they haven't returned to "the beacon." When they were last on Nerva - in "The Ark in Space" - it was referred to as a space station. It doesn't become Nerva beacon until the next episode.