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.
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: 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: After Lucy tells Ethel her plans for gluing on a mustache, Ethel congratulates her on the crazy idea, and in the next shot of Lucy in her bedroom just as she opens the door for Fred and Ethel, a crew member's arm moves into the shot at the right side of the screen. (00:06:15)
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.
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.
Continuity mistake: After spending the night at the hotel, when Ricky goes to the front desk to speak with the "Justice of the Peace" it's 7:30 on the wall clock. Then, when Mr. Willoughby stands by the stairs and calls to his wife it's almost 7:40, but when Ricky gets ready to propose it's 7:30, but it's 7:45 when Mrs. Willoughby comes downstairs in the closeup, then back to 7:30 in the wideshot. (00:17:40)
Visible crew/equipment: After Ethel tells Lucy that she lives dangerously, when Lucy mentions the incident at the carnival the year before, the shadow of the moving boom mic is visible at the right, by the window. (00:01:45)
Visible crew/equipment: When Lucy opens the closet door to show Ethel all the donated stuff for the bazaar auction, the boom mic (appears to be a double mic) dips down into view at the top of the screen (not visible in some streaming versions). (00:02:25)
Revealing mistake: When Ricky brings home the psychiatrist, in all the long shots of the living room from the time Ethel walks around the coffee table toward Fred, we can see that all four coffee table legs have been propped up on stone blocks.
Audio problem: During various shots in the Ricardo living room one can plainly hear what appears to be the whirring of the camera.
Cuban Pals - S1-E28
Visible crew/equipment: Right after Lucy phones for a cab the doorbell rings, and when she opens the door for Fred the cabbie, the shadow of the moving boom and mic appear on the kitchen door. (00:17:20)
Cuban Pals - S1-E28
Visible crew/equipment: When Renita rings the doorbell, just as Lucy opens the door the shadow of moving equipment (likely the boom mic) is visible at the top of the screen, between the kitchen door and front door.
Lucy Does a TV Commercial - S1-E30
Visible crew/equipment: In the scene where Lucy supposedly stumbles on a few minutes before hand because she is drunk from the Vitameatavegamin, you can see a sliver from her living room in the backstage area.
Lucy Gets Ricky on the Radio - S1-E32
Visible crew/equipment: At the start, after Fred and Ethel walk in, when Lucy and Ethel walk away from the kitchen shutters carrying things, the stage microphone and stand can be seen at the right side of the screen. (Later in the episode, when Lucy and Ricky appear in the quiz segment an identical microphone is on stage with them). (00:00:35)
Visible crew/equipment: When Lucy and Mrs. Littlefield bring out the soup and then salad, at the start of the shots just as they leave the kitchen, the shadow of another camera can be seen on the edge of the set's "wall" at the right side of the screen. (00:20:25)
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."
Deliberate mistake: In episode "Redecorating" Lucy wins new furniture, then in the next episode "Ricky Loses His Voice" the new furniture's delivered to the apartment, and the new couch has two normal and identical seat cushions. Starting in the next episode "Lucy is Enceinte" until the episode "Lucy Wants New Furniture", in some scenes the couch has the identical short cushions, however, in other scenes one of its seat cushions (depending on the episode, it's either left or right) is much higher than the other. For example, in "Lucy Hires a Maid" the higher seat cushion's on left side while Lucy waits for her lunch, then after Ethel urges Lucy to fire the maid the short cushion's on the left. The uneven cushions are usually seen in scenes with either Desi or another male actor, who sit on the side of the couch which has the higher seat cushion. There are even scenes where both of the seat cushions are the higher ones, such as in "Lucy's Last Birthday."
The Anniversary Present - S2-E1
Deliberate mistake: In this episode Lucy is trying to get Ricky to notice that their anniversary is on Monday the 19th by showing him a large calendar with the 19th circled. However, when they are in California and they celebrate their anniversary and Ricky asks for information to be wired to him, the telegram tells him that their anniversary is on the seventh.
Continuity mistake: When Lucy handcuffs herself to Ricky we see the style of handcuffs as they phone the locksmith, but when they're both in the bedroom their handcuffs are entirely different, then their handcuffs revert to the original style when the locksmith shows up. Additionally, when Lucy cuffs Ricky's wrist note the direction of the locking bar around Ricky's wrist, but the next morning when the locksmith is with them, the locking bar is around Ricky's wrist the opposite way, which is quite impossible. (00:06:45)