Revealing mistake: When Frasier comes into the chalet after skiing he doesn't show any of the visible effects after a hard day on the slopes. Meaning, his face isn't even flushed from the cold, his hair is perfectly combed after wearing a hat and there is not even a drop of snow on his boots.
Plot hole: Laura successfully knocks out both bad guys, steals their van and crashes through the warehouse doors. The van doesn't stall, but inexplicably, she stops it, gets out and runs away on foot, even though the baddies are coming to and coming after her. Not the option you'd expect a kidnap victim to choose: most people would floor it and keep on driving. (00:23:40)
Character mistake: When Alex mentions to Mallory that he's had sex before, he tells her he was 17 and that it was leap year. Not correct, this event occurred in 1982 (during one of the first episodes when Alex was 17), which was not a leap year.
Factual error: There is an intercom system in the library that is used by Derek (and at the end, Edward). They try pushing down the buttons to talk (which is normal for intercoms), but then each time, we are hearing Ricky and his grandfather's conversation from inside the car that's outside without using the intercom connected to the house. In the 80s, a house intercom system would not pick up a conversation in a parked car outside.
Visible crew/equipment: When Stephanie leaves the dining room a boom mic is visible. (00:11:04)
Testimony of Evil (Dead Men Don't Laugh) - S1-E6
Continuity mistake: At the start, the glass on the left is poisoned. The guy picks up the glass on the right, but still ends up dying.
Up the Crick Without a Piddle - S7-E4
Visible crew/equipment: While Madam Fanny is rehearsing at the piano, behind her in the background, a woman comes down the stairs. It is not a waitress, and Rene and Edith are still in London.