Continuity mistake: The fireplace moves from episode to episode, from the center of the room to the corner.
Revealing mistake: When Martin uses telepathy to tell George's girlfriend how to open the window, the two wires attached to the bows on the dog's floppy ears are visible. (00:05:05)
That Little Old Matchmaker, Martin - S1-E12
Character mistake: In Bill's office, after Tim talks about the acoustics in the building, Bill calls Tim "Bill." (00:15:51)
Oh, My Aching Antenna - S1-E33
Continuity mistake: Even though Tim and Uncle Martin live on the 2nd floor at Mrs. Brown's above the garage, every view outside the living room window with the sheer drapes shows the house across the street from a ground floor perspective. This happens in multiple episodes.
When You Get Back to Mars, Are You Going to Get It - S3-E24
Visible crew/equipment: When Tim and Martin are carrying Andromeda to the bedroom and Martin opens the door with his Martian finger, the crewmember actually opening the door can be seen on the hinged side of the door. The crewmember continues to move in that space for about 3 seconds during the scene. (00:10:00)