Continuity mistake: Near the end of episode three, Jamie starts to read the printout. At first, he is reading the printout the right way round. But when we next see him, he seems to be reading it upside down. Then the third time we see him, he is back to reading it correctly (right way up).
Continuity mistake: When the TARDIS breaks apart and the console sent spinning off into space, Zoe is lying on it. In close-ups she lying on her left side facing towards Jamie (who is opposite), but in the distance shots done with small models, she is lying on her right side facing away from Jamie.
The Invasion - S6-E3
Audio problem: The first victim of the hypnotic signal stops walking when he hears it, but the sound of his footsteps continues for several seconds afterwards.
The Invasion - S6-E3
Revealing mistake: The Cyberman that falls from the roof in the final episode is obviously an empty costume. (This is another example of a mistake being repeated from an earlier episode. See the earlier story "The Tomb of the Cybermen" for a note about the same 'revealing' mistake happening).
Visible crew/equipment: Episode 5, while Zoe and Jamie are at the Weather Control Station, when they hear the Ice Warrior approaching they both hide, and the actor's T-mark is visible on the floor. (00:18:00)
Revealing mistake: When Slaar discovers the video link is operational and being viewed on Earth, in the closeups of Slaar we can see the edge of the reptilian mask and the actor's real human neck. (00:20:40)
Continuity mistake: Patrick Troughton's sideburns keep appearing and disappearing, depending on whether what is being shown is location filming or studio.
Revealing mistake: When Jamie is wrestling with one of The Ice Warriors in a storage room, one of them gives the wall an almighty knock and it nearly falls down.
Visible crew/equipment: While The Doctor and Zoe are on the SIDRAT, The Doctor expresses hope to get the hang of its controls. When the SIDRAT materializes, in the shot facing the door as The Doctor pokes his head out to exit, the camera turns toward the right and there's a reflection of the moving camera and the camera operator walking behind the camera, at the right side of the screen. (00:08:25)
Revealing mistake: Episode 6, while in the barn Von Weich asks Moor (played by David Troughton, son of Patrick, who plays The Doctor) to retrieve the monocle in his pocket. Then, when Von Weich continues with his plan, in his closeups we can see a vertical piece of mesh tape over the actor's right eye. (00:13:05)
Character mistake: Despite being asked to memorise all the locations and war zone commanders, Zoe's photographic memory lets her down: her first words to the Mexican leader are 'Who are you?'.
Plot hole: The map of the "War Zones" where the Aliens are conducting their War Games can be seen several times in this story. The map is visibly divided into 11 zones. Yet, during this story, the "War Zones" visited or referred to total THIRTEEN.
Continuity mistake: The end of episode 7 does not match the reprise of the story at the start of episode 8. The Doctor, Security Chief and guards file into the SIDRAT in a different order.
Factual error: The Doctor meets Jamie at a time after the Battle of Culloden. But here Jamie says he met him in 1745. Culloden took place in 1746.
Revealing mistake: When the resistance are storming the landing bay, one of them punches at least a foot to the right of a guard's face, but he still collapses.
Audio problem: In episode 3, when the dog is barking at Sam's house and is abruptly silenced (apparently by an Auton), the sound is obviously not a dog barking. It sounds a bit like a man pretending to be a dog, and going "woof woof" not very convincingly.
Audio problem: When the Doctor arrives at UNIT HQ in his stolen car, he speaks to a guard. We see close ups of the guard twice...but watch the brief clip of the Doctor (Jon Pertwee) between the two and you can just see that his lips aren't moving even remotely in synch with the words. (In fact, it is just a repeat of the previous shot of the Doctor, with new lines dubbed in).
Revealing mistake: When the Doctor falls out of the TARDIS, near the beginning, he nearly manages to pull off the entire TARDIS door.
Audio problem: The music accompanying the closing credits fades down part way through (at a different point in each of the four episodes) and simultaneously fades up at a different point, the net result being a rather disjointed-sounding edit.
Other mistake: I know that regeneration causes the Doctor to change his appearance, but I didn't know it can produce a tattoo visible on the Doctor's right arm in episode 2.
Chosen answer: The Master is insane. If he can't control the universe, he'd rather see it destroyed.
Captain Defenestrator