Revealing mistake: In episode 1, one of the windows on the Tardis is leaning in, but by the time we get to episode 6 it has managed to fix itself. Also when the bridge falls down you can see the poster through the gap, showing that there is no back to the Tardis.
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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.
Plot hole: The energy weapons in this story fire a series of small red bullets, which cause numerous problems. For a start, the guns appear to have seven chambers, yet the bullets start from the same point; as they are separate bullets, surely the most minor of movements would mean they wouldn't emerge in a straight line. Later, when the Doctor steals a cart, the bullets are coming quite a distance towards the screen but the bullets don't get any bigger. Also, in the same scene, the Doctor passes through the area they seem to be travelling, yet the bullets just continue to pass in front of him.
Plot hole: The Bandrils not only know of the Time Lords but are capable of connecting to them, yet the Bandril are barely capable of space travel and can't produce their own food. So, the Bandrils are not very technologically advanced it seems, so why do they have ties with the High Council of the Time Lords? And how does either party benefit from such an association?