Continuity mistake: During Rod Serling's opening narration you can see over his shoulder part of the outline of the portal to the 4th dimension, which would be drawn there later in the story.
Continuity mistake: The hundreds of ropes used by the tiny people to pull down Craig's statue vanish in the next shot, when the statue hits the ground. (00:23:55)
Hocus-Pocus and Frisby - S3-E30
Visible crew/equipment: When Frisby tells the two travellers that they're looking at the grandad of the American automobile, we can see the reflection of a crewmember wearing a suit, possibly the director, who stands up from a directors chair (also seen in a following shot). Then as Frisby tries to locate the gas tank, the shadow of the moving boom mic is visible on the store's doors. (00:06:20)
Hocus-Pocus and Frisby - S3-E30
Visible crew/equipment: After the two travellers have paid for their gas, when Frisby advises them to check in someplace because of the clouds, the reflection of the moving boom pole and mic can be seen above the word "shop" on the store window. (00:08:00)
Hocus-Pocus and Frisby - S3-E30
Revealing mistake: Make-up for the space aliens was apparently changed after the closing scene in the store was shot and before any footage of the aliens' "true appearance" was actually taken. This resulted in Frisby, who is now telling the truth and finding no one to believe him, saying that the aliens had a single eye in their foreheads, when in fact, the aliens each had two eyes, in the traditional location. (00:24:00)
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.
In His Image - S4-E1
Revealing mistake: In the basement lab scene at the end, George Grizzard's double's face is visible in profile several times. (00:38:50)
The Thirty-Fathom Grave - S4-E2
Factual error: On the bulkhead of the ship's sickbay is a standard 12-hour civilian clock. It shouldn't be there. All clocks aboard U.S. Navy vessels show 24-hour military time. (00:31:20)
Revealing mistake: We see Redfield's car strike the invisible barrier from a side angle. It jerks to a stop and the hood flies up, but there's no other front end damage - until the angle shifts to a forward view, a shot of an identical car that had been previously wrecked. Now there's suddenly considerable damage to the front end, and the hood is in a different, much more crumpled position. (00:11:10)
Continuity mistake: As Ilse walks toward the front of the classroom, she passes the kids in the last row and is even with the kids in the next-to-last row, but in the following shot, shown from her point of view, she's passing the kids in the last row again. (00:30:45)
Death Ship - S4-E6
Revealing mistake: When Mason puts the ID card back into the pocket of his dead duplicate, the "corpse" twitches its eyelids. (00:14:30)
Death Ship - S4-E6
Visible crew/equipment: Just after the ship re-attains orbit, the shadow of a production crew member moving his arm can be seen on the wall at the upper right of the shot. (00:38:30)
Death Ship - S4-E6
Visible crew/equipment: In the final shot of the ship ascending into space, one of the filament lines supporting the model is showing just above the saucer. (00:44:15)
Continuity mistake: When Jackie leaves the office, the clock reads 10:12. The ensuing continuous scene with Winter and Mr. Smith is almost 6 1/2 minutes long, yet at its end, the same clock has advanced only 2 minutes, now reading 10:14. (00:33:00 - 00:39:15)
No Time Like the Past - S4-E10
Factual error: The U-boat has a spinning sonar mast. Subs in 1915 didn't have that.
Continuity mistake: When Mr. Ferguson is measuring the wax figures, he's shown holding a tape measure up against the figure of Landru (the one holding the rope). In the next shot, the figure is shown with no one near it. The next shot again shows Mr. Ferguson measuring the figure. (00:45:35)
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.