Plot hole: A block of cement that big would be very heavy, far too heavy for Lucy and Ethel to carry, not to mention someone would have noticed them carrying back to their hotel room.
Revealing mistake: Lucy, Fred and Ethel are admiring the celebrity footprints in cement outside Grauman's Chinese Theatre in Hollywood. In several scenes, the shadows cast by Lucy, Fred, Ethel and a passerby make it very obvious that what appears to be the ticket office, entrance and front wall are actually just a painted backdrop.
Visible crew/equipment: When Ricky is with John Wayne in his dressing room at the studio, getting yet another set of footprints on the block of cement, three T-marks are visible on the floor. One of those T-marks can be seen closeup when Wayne is lying on the table for his rubdown. (00:18:10)
Visible crew/equipment: When Ethel walks into her hotel room and tells Lucy and Fred about having to push the motorcycle to three different places, the second camera (or other equipment) keeps moving in and out of shot at the right side of the screen. (00:13:00)
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.
The Great Train Robbery - S5-E5
Revealing mistake: When Ricky and Lucy find their train compartment, while they stand outside their door talking we can see the actor playing the porter peeking out of the next compartment's door waiting for his cue, and in a few moments he opens the door just as Lucy approaches. (00:02:20)
Homecoming - S5-E6
Visible crew/equipment: During the episode a small tape mark is visible on the floor between the coffee table and the couch, and a T-mark can be seen on the floor near the desk, such as when Lucy starts telling her guests about their "fabulous" trip, Ethel stands at the T-mark and a female guest stands at the tape mark. (00:07:05)
Homecoming - S5-E6
Revealing mistake: In the scene in the Ricardo's kitchen, after Fred enters through the rear entrance the door is left open. Through the doorway one can see at a certain point, not just the NYC real estate in the distance but apparently a blown-up photograph of what "appears" to be a man and woman sitting at a small table in a cafe. However, in a subsequent episode of the same view through the rear door it appears that the exact same background photo shot may actually be, not a man and woman but features on the outside of a building, such as one or more windows.
The Ricardos Are Interviewed - S5-E7
Continuity mistake: When Ricky's new agent insults the apartment building Ricky explains that Fred and Ethel are their best friends, and we see Lucy drop the toy train onto the chair and take hold of the jack-in-the-box toy (in the crook of her left arm) with her right hand, but when it cuts to the closeup the toy train is back in Lucy's right hand and the jack-in-the-box toy is once again held in her left arm. (00:03:50)
The Ricardos Are Interviewed - S5-E7
Visible crew/equipment: When Ricky's new agent stops by the apartment to talk to him, Fred and Ethel are standing in front of the desk, and there's a T-mark on the floor in front of Ethel's feet. (00:04:50)
Continuity mistake: When Ricky comes over to Lucy, Fred, and Ethel after he sings for the first time, his hands are by his sides. The shot changes his hand are now in his pockets.
Continuity mistake: When Lucy is talking about finding an undiscovered artist she is holding a French dictionary. The way she is holding the dictionary changes a couple of times.
Lucy Gets a Paris Gown - S5-E20
Visible crew/equipment: Lucy is walking around the living room, assembling a sandwich from food she's hidden in various places. When she tells Ethel that they're low on lettuce, the shadow of the boom mike is visible behind her.
Lucy Gets a Paris Gown - S5-E20
Continuity mistake: When Lucy and Ethel are sitting at the table at the cafe just before Ricky and Fred show up, Lucy starts to put her arms on the table. The shot changes and her arms are already on the table.
Lucy in the Swiss Alps - S5-E21
Other mistake: The Ricardos and Mertzes are trapped inside an abandoned cabin after it is buried by an an avalanche. They are rescued by an oom-pah band playing "La Cucaracha." When the band members enter the cabin, their clothes and shoes are completely dry, and they don't track in any snow or water. Then when the Ricardos and Mertzes follow them out of the cabin, they leave their backpacks behind.
Return Home From Europe - S5-E26
Continuity mistake: As Lucy gets up from her airplane seat holding the big hunk of cheese wrapped in a blanket she is masking as a baby, it bends in half as if it were already cut. This is the scene before she sneaks off to the kitchen to cut it apart. In prior scenes, the cheese is intact and solid. (00:17:10)