Children of Earth: Day Two - S3-E2
Character mistake: When lanto is in the park and the children all stop the camera shifts to look at a little girl in pink. But in the top left corner there is a young blonde girl still moving and looks to be silently mouthing a word as she steps off the roundabout. (00:32:08)
Children of Earth: Day One - S3-E1
Character mistake: Lois says that Colonel Aduya's uniform "isn't British Army". In fact, it is entirely (and accurately) British Army with the exception of the small UNIT badge over the pocket.
Cyberwoman - S1-E4
Character mistake: In this episode Jack tells Gwen that he does not sleep, yet the next episode, Small Worlds, begins with Jack asleep and dreaming of the day his comrades died on a train, with rose petals in their mouths.
Answer: He might have requisitioned or stolen it from Torchwood London, or he might have been ready down below once it'd been severed, searching for "the right Doctor" and not knowing that the newly-regenerated Doctor was the one he was looking for.
Captain Defenestrator