Continuity mistake: When the decrepit Mr. Holt gets his new young body (briefly necessitating a different actor in the role), his German accent mysteriously disappears. He gets it back when he returns to his old body. (00:21:00)
Revealing mistake: At the end, though Williams is shot multiple times (by several rifles, no less), there's not a drop of blood on him and no holes in his clothes. Also, his "corpse" is visibly breathing. He's clearly meant to be dead, so the fact that he's an alien with healing powers does not explain why he's still breathing - or why the bullets left no holes or blood on his clothes. (00:22:30)
Continuity mistake: When we first see it, the grandfather clock is stopped at 2:33. But when Alex opens the case to adjust and restart it, the clock reads 4:40, and he moves the hands to 2:33 after checking his watch. (00:01:05 - 00:03:50)
I Sing the Body Electric - S3-E35
Continuity mistake: When Tom races into the house, the exterior shot is of a front door with six window panels. But when we cut to the interior view of him coming inside, the door has suddenly become solid, with no windows at all. (00:13:20)
The Changing of the Guard - S3-E37
Continuity mistake: While at the window listening to the Christmas Carolers, the eyeglasses Professor Fowler is wearing disappear and reappear, depending on the camera angle.
Answer: It's explained in the episode. The aliens are experimenting to see how humans react to various scenarios. This just happens to involve them using super strength.
Thanks. It's been a long time since I saw the episode so I forgot.