Plot hole: In this episode, the Doctor is said to have died during the events of "The Runaway Bride." As a result, he was not able to prevent the spaceship Titanic from crashing in London. It is later shown that southeast England was obliterated by the explosion. This falls far short of what the Doctor mentioned in "Voyage of the Damned", wherein he frantically repeated that if the Titanic crashed, the drive's explosion would wipe out all 6 billion people on the Earth (that's the entire human race at the time of the show's airing).
Silence in the Library (1) - S4-E8
Visible crew/equipment: While the Doctor tries to get into the data core (after Proper Dave tried) it cuts to the telephone still ringing, and when the young girl asks her dad why he's not answering the phone, just as he tells her that the phone is not ringing the boom mic dips into view at the top of the screen. (00:19:40)
Continuity mistake: After the Master changes all humans into copies of himself and Wilf says, "What have you done, you monster!?", it goes to all the different Masters in the room saying, "Are you talking to me?" The Abigail Naismith-Master is shorter than the Joshua Naismith-Master. In another shot they are the same height. The Abigail Naismith-Master is wearing very high heels and should be taller than the other Masters. (00:56:00 - 00:56:50)
Continuity mistake: In the scene toward the end where the Doctor is shot by the Dalek, when the camera is shooting from Rose's point of view, the Doctor is gasping and struggling for breath. However when the camera shows the Doctor from behind, he's lying completely still in Rose's arms. The camera cuts back to Rose's POV and he's struggling again, with no time in between for the change in his movements. (00:43:35)
Other mistake: Martha falls into the bog and Hath Peck rushes down to help her. She calls out "Help me, Peck!" but the subtitles read "Help me peg!" This is just one of many errors in this series' subtitles, which seem to have been added by listening to the dialogue without reference to the script. (00:26:30)
Factual error: When the Immortality Gate is activated, there's a wide shot of Earth as the wave from the device goes around the planet. In another instance of a mistake made by a few previous Christmas specials, despite this taking place on Christmas Day, the North Pole is looking very, very sunny for what's supposed to be the dead of winter. (00:54:50)
Continuity mistake: Near the end, when Luke teleports and switches places with the Doctor on the Sontaran ship, Luke catches the atmospheric converter's switch twice, once in the wide shot and then again in his POV. (00:40:25)
Continuity mistake: At the start, the first shot of Donna seated in the auditorium of Adipose Industries is flipped. The mole on her chin should be on the right, but in this shot it's on the left. (00:01:25)
Revealing mistake: When Torchwood is transmitting a signal to the Doctor, there is an overhead shot of Cardiff in which several shoppers are idly walking through apparently deserted streets. (00:31:55)
Revealing mistake: In the opening scene the Doctor and Donna are speaking over the phone. The purple phone Donna is holding shows the slot where a cable should be plugged in, but there is none. (00:00:25)
Suggested correction: This shouldn't be considered a mistake. While it's true in real life this phone has a slot for a cable, they're on an alien planet and this is unknown technology. In-universe there's no way of knowing what that slot is for, and there's no reason to think the phone needs to be plugged into anything.
Factual error: When the shot zooms out from Earth across the Solar System before revealing the narrator, Jupiter and Saturn are shown. Although scaling is somewhat exaggerated, Saturn appears to be closer to the Sun than Jupiter, which it most definitely is not in real life. (00:57:57)
Continuity mistake: When Gadget is driven to the TARDIS so the Doctor can retrieve it, the landscape around it is much flatter and without the large boulders strewn around the TARDIS when the Doctor arrived on Mars at the beginning. (00:52:41)
Continuity mistake: When the Doctor leans on the railing above the glacier while telling Adelaide about the Ice Warriors, he rests his left hand a ways out on the railing, in a spot where it should be visible but isn't in the next shot from behind him. (00:28:57)
Continuity mistake: When Martha arrives at Osterhagen Station 1, she unbuckles the belt of her teleport backpack, but in the wide shot immediately afterwards the belt is still buckled. In the next shot, it's back to being undone as she takes it off. (00:18:47)
Continuity mistake: When the Doctor, Rose and Jack get out of the TARDIS onboard the crucible, the console room is lit in very blue light. But in the shots of the console room before and after, it's lit completely differently. (00:09:15)
Continuity mistake: When the TARDIS is breaking through the time limit to reach the stolen planets, the console room catches on fire from the strain. But after reaching its destination, the console room is abruptly back to normal. (00:35:05)
Revealing mistake: When the Doctor and Donna run back inside the TARDIS to find the console room lit up in red and the Cloister Bell ringing, what's visible outside of the doors as they run in isn't the bright Shan Shen street the TARDIS is parked on but the dark soundstage the set was built in. (00:47:49)
Continuity mistake: After the TV signal cuts out due to the crash of the Titanic, when Sylvia says "It's gone dead" while searching for a channel, she moves her arm with the remote forward the same as she did in the previous, wider shot. (00:18:57)
Silence in the Library (1) - S4-E8
Revealing mistake: When the Doctor notices the unnatural triangular shadow signalling the presence of the Vashta Nerada and points it out to Donna, the shadow appears over Donna when she's standing in front of it, showing that it's a special effect added to the shot afterwards. (00:11:10)
Continuity mistake: When the Doctor finds the stolen cup inside Christina's knapsack, he's shown reaching for it twice, in the wide shot and the close-up. (00:38:40)
