Children of Earth: Day One - S3-E1
Revealing mistake: When the children are possessed by the 456, they're supposed to be frozen and stare blankly ahead. But during the second possession, as the camera is panning across a school playground, a boy on the far right is looking directly at it. As it moves closer to him, he swivels his eyes back to where they're supposed to be. (00:16:30)
Children of Earth: Day Two - S3-E2
Revealing mistake: When Ianto drops the concrete cell into the quarry and it breaks apart, the green foam from which it is made becomes visible. It is evident that the outside of the block was painted to resemble bricks and concrete block. When this breaks apart on the ground, the inside becomes visible, showing the concrete and brick textures are only surface deep. (00:53:05)
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