Deliberate mistake: The final Auton attack in this episode is supposed to take place in a busy London street, but it is a pedestrianised area, and several shots reveal this. For example, there are no road markings visible, no apparent distinction between pavement and road, and a bus stop appears to sit in the middle of the 'road'.
Deliberate mistake: When Jack is scanning the gas mask people, he has a scanner on his right wrist. However, when he shows Rose and the Doctor his image of the Chula warship, the scanner is on his left wrist. The makers flipped the stretch of film, according to the commentary, to make the shot work. (00:37:45)
The End of Time: Part Two - S4-E18
Deliberate mistake: When the Doctor visits all his recent companions before he regenerates, he goes to a book signing of A Journal of Impossible Things, written by Joan Redfern's great-granddaughter. When she is signing the book for the Doctor, you can hear the scratching effect from the pen but you can see that the pen isn't touching the paper. (00:59:50)
Deliberate mistake: When the Doctor is watching news broadcasts from around the world about the ghosts, the newspeople from France, India and Japan should be heard speaking English because of the TARDIS' automatic translation. (00:05:55)
Deliberate mistake: The young Amelia Pond (played by Caitlin Blackwood) has brown eyes, however her older self (played by Karen Gillan) has green eyes.
Last of the Time Lords (3) - S3-E13
Deliberate mistake: The Master uses his laser screwdriver to suspend the Doctor's ability to regenerate. While he is in fast motion, in a close-up you can briefly see Lucy's arms in fast motion as well. (00:12:20)
The Woman Who Fell to Earth - S11-E2
Deliberate mistake: The Doctor (Jodie Whittaker) is shown wearing the same clothes that the previous incarnation (Peter Capaldi) wore after regenerating. Peter Capaldi is 6' and Jodie Whittaker is 5'6", but the clothes fit perfectly. She even says her legs used to be longer, and yet the trousers aren't flapping around her feet.
Deliberate mistake: In real life, Viking helmets didn't have horns on them, because it would be a liability in combat. The horns were actually for drinking. The Vikings in this episode were given horns anyway, because the writers didn't feel it was worth having to include an explanation of hornless helmets to a general audience.
Deliberate mistake: The Globe Theatre is shown staging performances at night. In actuality, they performed during the day, when there was enough light, since this was pre-electricity. This was done both to make the climax of the episode scarier and because they shot on location in the real Globe, which still shows its plays during the day, and thus they didn't have a lot of time to shoot during the day there.
The Day of the Doctor - S7-E16
Deliberate mistake: Looking closely at the floor of Eleven's console room reveals that the part of the floor around the console facing the door has been discreetly raised up, which it isn't in any other appearance of this console room, so that Clara can ride her motorcyle inside it without going down two steps. This wasn't in any previous episode and is gone in the next one.
Suggested correction: The Tardis has constantly shown it can change its internal structure to fit its needs or desires.