Continuity mistake: When Lucy crawls into the New Neighbors' apartment she's startled by the stuffed bear head, and in the closeup of the bear head it's in front of a bare wall, but in the rest of the shots it's in front of furniture. Additionally, other things change as well between shots: the books under the bear, the hat, etc. (00:10:15)
Visible crew/equipment: When Ethel's reading aloud from the book while Lucy's standing beside her in the living room, the shadow of a crew member can be seen moving around on the surface of the desk's back. (00:04:25)
Continuity mistake: The step up into the kitchen is no longer there in later shows such as "The Fur Coat" and others.
Ricky Asks For a Raise - S1-E35
Character mistake: After Tropicana nightclub owner Mr. Littlefield replaces Ricky Ricardo with Xavier Valdez, "the Konga King," Lucy, Fred and Ethel try to get Ricky's job back by going to the nightclub in a succession of different wigs and costumes, then leaving when they learn that Ricky is no longer performing there. At one point, Fred and Ethel enter the nightclub, posing as "Mr. And Mrs. Crumley." A disguised Lucy enters one minute later and is outraged to hear that Ricky is no longer there. Ethel then pretends to phone a friend to tell her to not come to the nightclub. Lucy says, "Attagirl, Mrs. Crumley." However, when Ethel had told the maitre d' she had a reservation for "Crumley," Lucy had not yet entered and therefore should not have known that name.
Suggested correction: During the point when Mrs. Crumbley wants to call her friend to get her friend to cancel her reservations as well, Mr. Littlefield says, "But Mrs. Crumbley," to protest as she walks to the phone to make her call. So he did say her name in front of Lucy, thus giving her the name to reply with, "Attagirl, Mrs. Crumbley."
The Adagio - S1-E12
Visible crew/equipment: Crew member shadow is visible at the foot of Ricky's bed near the end.
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.
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.
Audio problem: During various shots in the Ricardo living room one can plainly hear what appears to be the whirring of the camera.
Plot hole: Both couples have the same group of friends and they were all invited to both going away parties planned on the same night at the same location. Isn't it likely that at least one of the main characters would have found out about the other party? But at the end, all seem surprised about the other party that was planned for them.
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.
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. 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.