Revealing mistake: In the end part of this story, in the large spider's den, the string supporting it is visible.
Deliberate mistake: In episode 3 of 'The Web Planet' (titled 'Escape To Danger') watch as one of the Zarbi operators, his vision impaired by the costume, runs right into the camera. So far behind schedule was the recording of this episode, however, that this mistake was retained in the finished episode, as there was no time left for a re-take.
Visible crew/equipment: In the scene where Ian's pen vanishes, as he checks to see if he is being followed you can see a boom mic shadow on his coat.
Visible crew/equipment: At the beginning of episode two, the Doctor finds Ian unconscious with a very obvious shadow of the camera and cameraman looming over him.
Visible crew/equipment: In an early TARDIS scene, at one point the cable powering the console is seen running from the base and under the wall.
Visible crew/equipment: At the end of episode 3, a venom grub starts chasing Ian. As it enters the screen however, you can see the actor under it crouching down.
Answer: TARDISes are generally available for properly authorised use on Gallifrey; they're not usually assigned to a particular Timelord on a long-term basis. The Doctor stole his when he left his homeworld.
Tailkinker ★