The Cemetery - S1-E1
Continuity mistake: From the inside view of the window the Hendricks gravestone and the family name is visible on it. From the outside view of the window the gravestone and the Hendricks are facing away from the window.
Continuity mistake: In episode 64, "For Whom The Bell Tolls. And Tolls. And Tolls", Tracy is shown seated at the table with a bowl of cereal - but in the shots immediately before and after, she's not there, nor is there any food at her place. (00:01:10)
Plot hole: The alien-possessed Mason steals Captain Lauritzen's fingerprints by pressing his fingertips to the captain's and "heat transferring" the prints. Big problems here: those prints would now be backwards and for the wrong hand. But when the computer later reads the prints, it fails to notice this and passes him through security as "Identity Correct." (00:23:30)
Continuity mistake: In an episode fairly late in the life of the show, Lou Grant says that when Mary came to interview for a job at the station, she bumped into the desk in his office and said, "Excuse me" to the inanimate object. However, we saw that interview in the very first episode, and no such thing happened.
Kitten Kong - S2-E7
Revealing mistake: When the Goodies are at the park with their animals, Graeme tries to teach his tortoise tricks. When the tortoise jumps, you can see the wire making it 'jump'.
The New Car - S4-E6
Audio problem: When Felix and Oscar are driving around looking for a parking space, Oscar says "let's sell the car." Felix then begins talking but no audio is heard, then an overdub of him saying "Are you crazy?" which doesn't match his lips.
This Must Be the Alamo - S4-E5
Continuity mistake: When McCloud and Broadhurst are driving around in the squad car, the vehicle changes in their closeups. Note the light atop the hood, the stickers with the police and unit number on the hood, the rearview mirror's vanishing act, etc.
Audio problem: Billie says her line "he needs a new image" without moving her lips.
Firefly, Light My Fire - S1-E1
Continuity mistake: Joy exits her house twice: once after the curtains pull back, then a second time after Harmony says his line.