Revealing mistake: Mr. & Mrs. Castle wish for a million dollars in 5 and 10 dollar bills. But the bills they receive all have the same pattern printed on both sides, a pattern which which doesn't resemble any real US currency. There's also not nearly enough of the bills to total a million dollars. (00:12:30)
Nervous Man in a Four Dollar Room - S2-E3
Revealing mistake: The main character's reflection in a mirror has come to life and much of the episode is a confrontation between the character and his reflection. Although they made an effort to reverse the image (the reflection wears his watch on the opposite hand and he bites his fingernails with the opposite hand) they forgot to reverse the buttons on his shirt.
Nervous Man in a Four Dollar Room - S2-E3
Revealing mistake: When Jackie pulls the wardrobe from the wall and spins it around, The Mirror briefly reflects an area beyond where the set ends.
A Thing About Machines - S2-E4
Revealing mistake: When the electric razor is coming down the stairs after Finchley, the wire used to pull it is visible. (00:19:50)
A Thing About Machines - S2-E4
Revealing mistake: When Finchley smashes the TV, the screen image stays visible for a short time after the screen is broken, revealing that the screen's image was superimposed.
A Thing About Machines - S2-E4
Revealing mistake: When the car is approaching the pool to push the man into the water, the tires tracks are visible in the grass, showing that the car had already made that trip. Either tracks from an earlier take, or the scene was filmed and then played in reverse, to be safe for the actor.
The Eye of the Beholder - S2-E6
Revealing mistake: In the episode, all the people are shown from the neck down to hide their faces (which at the end we see this is on another planet as they are alien looking). But as the first nurse seen in the episode walks to the window and turns around, even in shadow you can see that she is normal looking, that is, no prosthetic or make-up applied for the alien effect.
A Most Unusual Camera - S2-E10
Revealing mistake: The crooks in this episode appear to have obtained the same pile of funny money that the Castles received in "Man in the Bottle." The bills don't even vaguely resemble any real U.S. currency. (00:20:25)
Revealing mistake: The sky behind the hanging scene at the end has several prominent wrinkles in it, betraying the fact that it's not a sky, but a cloth backdrop. In some shots, you can also see shadows on the cloth. (00:19:00)
Revealing mistake: The woman leads a simple but hard life, however, in several close ups, she has long, tapered, finely manicured and polished fingernails.
Revealing mistake: When the old lady touches the door handle right before getting cut by the knife she gets paint smeared on her hand from the door handle before being cut with the knife.
Mr. Dingle, the Strong - S2-E19
Revealing mistake: Dingle lifts the bar bully over his head and twirls him around. But The Dummy used to achieve this effect has a distinctly lifeless, plastic face, and more than once, the wires suspending it are visible. (00:18:00)
Mr. Dingle, the Strong - S2-E19
Revealing mistake: When Mr. Dingle lifts the bench, you can see the cables holding it up.
Mr. Dingle, the Strong - S2-E19
Revealing mistake: When the reporter is talking into the microphone, you can see that the microphone is not hooked up.
Mr. Dingle, the Strong - S2-E19
Revealing mistake: A close-up shot of the man Dingle is lifting over his head shows part of the lifter's face - revealing that an actor other than Burgess Meredith is used here.
Mr. Dingle, the Strong - S2-E19
Revealing mistake: Before Dingle tries to lift the building, a crack can already be seen in the ceiling beam.
Revealing mistake: In the boarding house hallway, Ed yanks the pay phone's receiver off the hook - and the entire wall to which the phone is attached wobbles. (00:11:00)
Revealing mistake: When Jimbo lifts the bed up using his mind, you can see the cables pulling it up.
The Rip Van Winkle Caper - S2-E24
Revealing mistake: The suspension machines are nothing more than large terrariums, there doesn't seem to be any electronics or piping or machinery of any kind attached to them.
Will the Real Martian Please Stand Up - S2-E28
Revealing mistake: As the Venutian asks the Martian to play music, the edges of the fake skin around the third eye is visible.
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.