Evolution of the Daleks (2) - S3-E5
Visible crew/equipment: As the Daleks present Sec in chains on the theatre stage, a stagehand is briefly seen moving behind them.
The Family of Blood (2) - S3-E9
Continuity mistake: As the scarecrow-soldiers advance on the school to do battle, the scene cuts to Sister of Mine, looking out from a school window. There is heavy rainfall outside. When we immediately cut back to the advancing scarecrows, it is a cold, clear night. (00:10:00)
Other mistake: Joan puts her stethoscope in her ears backwards when listening to John Smith's single heart.
The Sound of Drums (2) - S3-E12
Factual error: When introducing himself to the Toclafane, President Winters refers to himself as "President-elect of the United States of America." President-elect is the title given to the victor of an American presidential election who has not yet been sworn in, between early November and January 20. This was a mistake on Russell T Davies' part, as he was under the impression it was a longer, formal title for the American president. (00:37:40)
Time Crash - S3-E15
Continuity mistake: At the end of "Last of the Time Lords", the Doctor flicks two switches on the console just before the Titanic hits. In the same scene in "Time Crash", the last control he hits is a large button.
Other mistake: When the Doctor and Martha are in their bedroom, there are many candles lit. Later, when Martha blows out one candle, the whole room goes black.
Suggested correction: When Martha blows the single candle's flame out and it goes black, it's not their whole room going black, it's the screen that does a "cut to black" to effectively terminate the shot. This instantaneous dramatic transition punctuates Martha's extreme annoyance with the Doctor.
Suggested correction: This is a common film technique, as audiences aren't exactly interested in watching someone walking around the room blowing out candles. She just probably blew them out later, and the pitch black is just showing that part of the room is dark now.
This explains why the mistake exists, however its still a valid mistake despite there being an explanation for it.
Continuity mistake: When the TARDIS arrives back from the formation of the Earth, the Doctor and Donna rush out leaving the TARDIS door open. And yet in the very next shot, the door is closed. (00:44:30)
The Sound of Drums (2) - S3-E12
Factual error: The army shoot at Martha's car and you can see sparks where the bullets bounce off her windscreen. But, at that close range, one of those things can go through a brick! I know you're supposed to allow a bit of disbelief, but this is taking it too far.
Revealing mistake: In the close up shot of the boys' machine guns firing, in the background a white truck can be seen driving across the green countryside; not appropriate for the time period of the story. (00:25:25)
Continuity mistake: When Lawrence is watching the Weeping Angel, just after seeing the Doctor's film/Easter egg, he turns away for a split second. By the time he turns back, you see the Weeping Angel's face only inches from Lawrence's face. But you then cut to a wide shot where you see the Angel's arms outstretched, so its face is about half a metre away from Lawrence's face. (00:34:45)
Continuity mistake: When Mr. Copper is talking about how space-lane fraud could get him ten years in jail, the cut on his forehead changes sides, as does the panel behind him, revealing the shot to be flipped. (00:36:25)
Daleks in Manhattan (1) - S3-E4
Continuity mistake: When Diagoras is seen being merged with Dalek Sec, he has gloves on, but when the hybrid Sec emerges, the gloves are gone. (00:45:00)
Factual error: A reflection of a full Moon is shown near the end. When Earth is viewed from the Moon earlier, over half of it is illuminated by the Sun. For it to be full Moon, the entire Earth would have to be dark. In addition, the place where the hospital was transported to was dark, and not sunlit. (00:37:45)
Suggested correction: When the reflection of the full Moon is viewed it is night time several hours after we saw the Earth from the Moon.
Yeah, no, the phases of the Moon don't work like that. New Moon and Full Moon are two weeks apart. Since the Moon appears to be, judging by the appearance of the Earth, between New and either First or Last Quarter, it is impossible for a Full Moon to be visible later that night.
Continuity mistake: In the scene when Donna asks the woman if she could borrow £10 because it's Christmas, you can see that Donna is wearing sports shoes instead of her usual white wedding shoes. (00:10:05)
Suggested correction: No, she's wearing the same shoes if you pay attention.
Never mind - she is wearing running shoes for no apparent reason.
The Sound of Drums (2) - S3-E12
Continuity mistake: When the Master stands up on the Valiant to announce that he is the Toclafane's "Master", President Winters is visible in the background, only the Toclafane aren't there. In the next shot, they return, buzzing around Winters' head.
Suggested correction: This seems to be caused by angles - the Toclafane are floating fairly high up, around the level of Winters' shoulders and above, but the Master is lower down. Hence, why they're not visible in the shot.
Character mistake: When the Doctor is taking Donna to 4.6 billion BC to watch the formation of the Earth, he says that it is the furthest back the TARDIS has ever been. But in the 5th Doctor episode "Castrovalva", the TARDIS drifted to 13.2 billion BC and the formation of the galaxy. (00:40:35)
Factual error: The Globe has (and had) 20 sides, not 14.
Character mistake: David Tennant has a strong Scottish accent, and puts on the Doctor's English one. When David and Freema Agyeman are lying on the bed in the hotel, David forgets his English accent when he says, "There's something I'm missing, Martha."
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)
Plot hole: The Doctor leaves Martha a recording with instructions for her for when he's human. However, the flashbacks to the incident that led to him using the Chameleon Arch don't leave enough - or any - time for him to have made the recording, presenting his decision to use the device as a spur-of-the-moment one that he immediately acts upon.
Suggested correction: He would have been planning the change to human for a while now, not just made it up on the fly. So he could have made a recording before the opening scene.
The episode makes it pretty clear that he and Martha got taken by surprise by the Family's attack. The Doctor also explicitly says, when he gets out the Chameleon Arch headset, that he never thought he'd use it. The flashbacks consistently present his decision to become human as one made as an urgent, in the moment one.