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.
Hollywood Anniversary - S4-E24
Visible crew/equipment: After Lucy rushes out with the newspaper to tell Ethel about all the movie stars coming to the party, when Lucy returns to the suite and closes the door, we can see the arm of a crew member and a board with "DPI" (Desilu Productions Inc) on it, at the bottom right side of the screen, and a bit of equipment at the top right corner. (00:15:00)
First Stop - S4-E14
Revealing mistake: When the bed Lucy and Ricky are in moves as a train goes by look real close and you can see the wheels on it to help move it across the set piece.
Suggested correction: Not necessarily an error. My bed frame is on wheels.
Continuity mistake: At times Ricky wears his gold wedding band, and other times - especially at the Tropicana - it is missing from his finger.
Suggested correction: So he took it off while performing. I googled images of Desi and Lucy and you can see he wore a wedding band in real life. Therefore, taking it off while filming would have been a deliberate choice. It's only a mistake if the band appears and disappears within a scene.
The Adagio - S1-E12
Visible crew/equipment: Crew member shadow is visible at the foot of Ricky's bed near the end.
Other mistake: When Ricky comes home at 3:00 am, the toggle light switch is in the down position. Ricky places his hand over the switch plate and the room goes dark, but the toggle light switch is still in the same down position.
Character mistake: When Lucy and Harpo are doing the mirror routine, Harpo grabs the horn on his belt with his right hand. For Lucy to create a "reflection", she would need to use her left hand but she uses her right hand.
Revealing mistake: When Fred and Ethel come with parts of their apartment's ceiling on them look closely at Ethel. The piece on her left shoulder falls off revealing what looks like a velcro pad to keep it in place.
Continuity mistake: Here it's said by the Ricardos that Fred and Ethel have been married for 25 years. Problem is in Season 1's episode "The Girls Want To Go To the Nightclub" the Mertzes both say they've been married for 18 years.
Other mistake: Lucy walks out on the balcony and sees Van Johnson sleeping on a lounge chair by the swimming pool. The photographic backdrop shows automobiles, trees, mountains, the Roosevelt hotel and many other buildings of Hollywood but when Lucy goes to the pool and sits on the lounge chair next to Van Johnson, the background is just a plain painted backdrop with no cars, trees, mountains or buildings. This plain backdrop also appears in the episode with Harpo Marx.
Revealing mistake: When Lucy's pinned against the sink by her bread Ethel goes for a saw. If you watch the doorway you can see her shadow where she's being given the saw.
First Stop - S4-E14
Visible crew/equipment: The gang stop at the roadside diner was obviously shot in-studio as the bottom seam is quite visible behind the car, and the backdrop shakes a little when Lucy opens the car door.
The Ricardos Dedicate a Statue - S6-E26
Continuity mistake: When Ricky is angry toward Lucy that Little Ricky's pet dog Fred has not learned to be obedient he threatens to return Fred to the dog pound where he says the Ricardos originally got him. However, in episode "6-12", Little Ricky Gets A Dog" Little Ricky admits to Lucy that he got Fred from one of his playmates whose dog had puppies.
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.
Audio problem: During various shots in the Ricardo living room one can plainly hear what appears to be the whirring of the camera.
First Stop - S4-E14
Other mistake: When the Ricardos and Mertzes arrive the first time at One Oak Cabins and Cafe the full moon is amid the tops of the trees. When they arrive the second time the full moon is in exactly the same location amid the tree tops as the first time they arrived. Fortunately, hours later when they make their sneaky escape from the cabin and return to their car the moon is no longer in view.
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)
Plot hole: Despite the plot, Lucy couldn't be fooled by Jimmy and Timmy Hudson. True, they could be fraternal twins but not even Lucy could mistake them for being identical as one's got a higher voice and the other's shorter.
Plot hole: Lucy mentions if Ricky comes home by bus, cab, or subway then they win the bet. Problem is unless they live next to a subway she wouldn't know if he'd used it.
Plot hole: How does Lucy get back up to the apartment bound and gagged? It would seem impossible to hop up all those steps, possibly take several hours if not all night.