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.
Nick of Time - S2-E7
Continuity mistake: After dodging the vehicles in the street, Don notices the time as 3 o'clock, when the machine predicted something would happen. When they go back into the diner, his watch has the time as 10:10.
Nick of Time - S2-E7
Continuity mistake: Don Carter is holding a glass of water at the lunch counter. When the shot cuts to him and Pat, his hands are clasped together, empty.
Nick of Time - S2-E7
Continuity mistake: As Don and Pat leave the diner and another couple enters, there are two glasses of tea that have changed position on the table with the Mystic Seer, and two chairs have suddenly materialized at the booth they were using when the other couple arrive to use the Mystic Seer machine.
The Lateness of the Hour - S2-E8
Visible crew/equipment: As Robert is pouring Dr. Loren's drink, an equipment shadow moves across the top of Jana's head in the foreground. (00:08:20)
The Lateness of the Hour - S2-E8
Visible crew/equipment: The boom shadow intrudes briefly at the upper left of the shot as Jana stands at the window and says, "Rest in peace." (00:16:15)
The Lateness of the Hour - S2-E8
Visible crew/equipment: When Jana is screaming "No pain!" at the top of the stairs, a film crew member's shadow can be seen moving on the wall behind her. (00:22:30)
The Trouble with Templeton - S2-E9
Continuity mistake: When Booth grabs her, Laura's long string of beads breaks. When she starts dancing a moment later, though, they've somehow repaired themselves. (00:18:50)

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.
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)
A Most Unusual Camera - S2-E10
Plot hole: How did the brother know where his sister and her husband were located after he escaped and jimmied open their door? The couple was staying in a hotel and they acted like they hadn't seen him in quite a while when he appeared on the picture of him walking in the room. They said he couldn't possibly walk through the door because he's been in prison for a year already.
Audio problem: Throughout Corwin's scene with the two children on the street, and through Rod Serling's subsequent introduction to the episode, you can hear the loud hiss of fan blowers used to waft artificial snow onto the set. (00:04:50)
Visible crew/equipment: When Sykes opens the Sheriff's office door to leave, the "sky" outside has a very large equipment shadow on it, hanging over the building across the street. (00:05:10)
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)
Continuity mistake: Hunnicut puts a cigar on the bar rail when going to talk to a couple, but during the opening narration in the same spot, it's missing.
Continuity mistake: The laser burns on the back of the old woman's left hand disappear when the knife is slicing at her through the door. They return a few shots later, though. (00:10:30 - 00:17:30)
Continuity mistake: The flying saucer the old woman hacks to pieces with an axe is noticeably not the same one that lands in her attic in the beginning. A cruder version was built for the axing scene because the model used was a studio keepsake - the original spaceship from the classic sf film "Forbidden Planet." (00:23:00)
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.