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."
Continuity mistake: When the jet is preparing to land in 1939 New York City, the view of the crew from the back of the cabin forward shows the airliner captain wearing his headphones, but the next instant close up of him shows him not wearing the headphones.
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.
Continuity mistake: During the scene in the diner between Ross the Martian and Haley the Venusian, there are objects such as a napkin dispenser visible on the counter over the left arm of Haley, which then disappear in the shots over Ross' right arm.