First Stop - S4-E14
Deliberate mistake: When they are counting the yards to Aunt Sally's pecan pralines, they count down 300 yards, 200 yards, 100 yards so fast they would have to have been speeding pretty fast to go hundreds of yards within seconds.
The Benefit - S1-E13
Revealing mistake: There's suddenly an upright piano in the living room where Ricky's desk used to be.
Suggested correction: There's nothing sudden about it. The rearranging of furniture between episodes occurs often, and would only be a problem if it happens within a scene. From the very start of this episode, the card table is already at the center of the living room, with the couch pushed back toward the wall, and the desk is behind the couch (holding telephone, etc), up against the wall where the piano usually is in other episodes. Ethel asks Ricky about the sheet music on the piano, and he explains he's been working on a musical number for the show at the Tropicana. So, for this episode's ongoing musical storyline, the positions of the piano and desk have been switched. Nothing whatsoever makes it a revealing mistake. This occurs again a few episodes later in Breaking the Lease.
The Adagio - S1-E12
Character mistake: Lucy turns in for the night in full makeup and lipstick, instead of washing up.
Character mistake: When Fred, Ethel, and Ricky confront Lucy on what she wrote about them in her novel Ricky states "I'm so hammy I should go lie down between two slices of rye bread." This is incorrect. Lucy wrote "He turned into such a big ham you could stuff him with cloves."
Continuity mistake: The Mertz' check out of the hotel and are in the garage on a motorcycle. Later they are back in their hotel room with Fred napping in a chair with a hurt shoulder.
Suggested correction: Ethel and Fred checked out of room 317, intending to leave. Later, after their motorcycle crashed, Ethel and Fred checked back in and were given room 372 (time codes 00:09:05 and 00:12:15), so Fred (with his hurt shoulder) is napping in the chair in his and Ethel's new room. There's no continuity mistake.