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."