Factual error: Though this episode is set in then-present-day 1961, the fistful of prop money the bartender is holding is not contemporary. It appears to be copies of 1880s U.S. Currency, though it's been reproduced as smaller, 20th Century sized bills rather than the larger ones that were standard in the 1800s. All in all, not something his bar patrons would likely be paying the bartender with in the 1960s.
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.
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."
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.
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.