On Thursday We Leave For Home - S4-E16
Visible crew/equipment: As the men talk in the cave, the boom mic is plainly visible.
Stopover in a Quiet Town - S5-E30
Visible crew/equipment: After Bob and Millie realise the tree and the grass aren't real, when they head towards the town Bob calls out, "Hey! Hey, anybody here?" Then Millie adds, "Somebody," and the shadow of the boom pole/mic moves across the bottom of the screen. (00:14:55)
A Thing About Machines - S2-E4
Revealing mistake: After Bartlett Finchley escapes from the menacing electric razor, his car confronts him outside. When Finchley's car chases after him, there's nothing attached to the Lagonda, but when the car slams through the wood fence and into the wall of boxes, there's a full grille guard mounted to its front. Then the grille guard promptly vanishes. (00:20:30)
The Trouble with Templeton - S2-E9
Continuity mistake: At Freddie's speakeasy, when Laura lifts Barney's script from the table, she begins to fan herself. In the wide shot, the script's titled top page with corner diagonal stripes is gripped under Laura's four fingers, with the blank back page at her thumb. It cuts to a close-up, and now the script is gripped in Laura's hand the opposite way, with the top page at her thumb (the back page is blank).
The Trouble with Templeton - S2-E9
Visible crew/equipment: When Booth walks over to Laura and Barney at the speakeasy, the moving boom mic casts a shadow on the wood pillar behind Laura, at the top left side of the screen.
The Four of Us are Dying - S1-E13
Revealing mistake: As the men walk out of the alley, the block continues ahead of them. You can see it's a painted background.
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.