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.
Plot hole: The Sycorax begin speaking English for all of the humans because the TARDIS is suddenly activated when the Doctor wakes up. However, it is stated elsewhere in the series that the TARDIS only translates for those who have been in the TARDIS, which Harriet and her translator haven't.
Continuity mistake: Near the beginning of the episode, the Doctor and Jack destroy a Dalek who is inside the TARDIS. It is seen again later when the Doctor, Rose and Jack come back into the TARDIS after talking with the Dalek Emperor. Yet later when the Doctor is sending Rose home, there is no destroyed Dalek.
Continuity mistake: When Rose is sitting on a bench and she gets a news report on her phone, look at the top of the phone screen - it says the time is 11:35. However, several minutes later, when the Doctor and Mickey find Rose, the clock says it's only 11:36.
Continuity mistake: Near the end of "Silence in the Libary," a sweeping shot shows that they're standing between two freestanding bookshelves. But at the beginning of this one, when they're supposed to be in the same place, they're able to break through a wall into a separate room.
Plot hole: Davros said that the reality bomb would destroy all parallel universes. He fails in the Doctor's universe, but the Doctor said in an earlier episode that every decision creates a new parallel universe, like if Donna had walked out of the TARDIS with Jack, Rose, and the Doctor. She wouldn't have imbued herself with Time Lordness, so Davros would have succeeded. This means that all the universes, including the Doctor's one, should have been destroyed, because if the Reality bomb only succeeds in one universe, it would destroy all the others as well.
Audio problem: Just after the Doctor makes his appearance and Lynda tells him he's "in the house", she appears to continue talking to him but we never hear what she says; instead the scene cuts to the other two housemates complaining about the Doctor's sudden appearance.
xx:xx:xxChris in Texas
Continuity mistake: When Yvonne Hartman is showing the Doctor through Torchwood after leaving the TARDIS, she goes to push a door open into the main building with one hand, but when the camera cuts to them entering the building she pushes them open with two hands.
Other mistake: After the Doctor tells Bill that Heather's face isn't symmetrical, when he and Bill look into the "puddle" together the Doctor explains that instead of seeing her normal backwards reflection, she's seeing her face "the right way round." The problem occurs in the next shot of the Doctor and Bill seen in the puddle, because the "WOW!" patch on Bill's jacket is properly where it should be, but note everything else is actually backwards. Things such as Bill's color-block top and her denim jacket buttons are on the opposite way. Also note the Doctor's ring has switched hands. Presumably this shot was edited, and the "WOW!" patch was blurred on the left of Bill's jacket then digitally added to the right side, to give the appearance that it's "the right way round" as the Doctor said.
Add timeSuper Grover
Continuity mistake: At the beginning of the episode, the police are chasing the bus and they give the numberplate as starting with 'Whiskey zero four seven' (Or something similar). That is W047, yet later on when the flying bus comes through the rift in time/space, the numberplate is completely different. This is because whilst filming in Dubai, the original bus broke down and had to be replaced.
Continuity mistake: When the Doctor is shot and killed while trying to regenerate on the beach, he falls with both legs extended. When River, Amy and Rory run up to him his left leg is bent. The camera cuts away again, and when it cuts back to show the Doctor's body one more time both legs are straight again. In addition, his left arm changes position between shots, between stretched out pointing away from his body on close-ups to bent with his hand resting on his thigh in wider shots.
Continuity mistake: When they are back in the cemetery at the end, the Angel shows up right behind Rory. In the first shot facing Rory, as the camera zooms in on a close-up of the Angel, the Angel's right arm/hand is pointing straight out, and its left open hand is up in a grabbing position. After River asks where the hell it came from, in the Angel's next close-up and all subsequent close-ups, its arm/hand positions are reversed - left hand is pointing straight out and its right hand is up. Yet in every shot of the Doctor, River and Amy together, in the foreground we see the Angel's left hand is up in the grabbing position.