Continuity mistake: When the Doctor and Harry arrive in the cryogenic chamber, they walk around for some time inspecting the chamber and talking. Towards the end, they notice a green slime trail newly appeared on the floor. But the trail was visible in the very first overhead shot of the chamber.
Deliberate mistake: In episode three, the Doctor and Vira meet a half-changed Noah. He holds a gun on them, then drops it at Vira's feet and the door is suddenly closed. This is because the scene was originally longer and involved Noah begging Vira to kill him before the Doctor shuts the door. It was trimmed down to get it past BBC censors.