When Martha contacts the Crucible the way she is holding the key changes between shots from inside the station and the view screen on the crucible.
When Jack finds Mickey, Jackie and Sarah he fastens the studs on the cover of his Vortex Manipulator. When he hugs Mickey however, three of the four studs have come undone.
If as shown on screen the emergency temporal shift only carries one person, how would Dalek Caan turning up on Davros' command ship in the time war get Davros out of the time war? In order for this to happen, there would have to be a second emergency temporal shift generator in Davros' chair.