Plot hole: In some episodes Lucy can not sing at all. In other episodes she can sing.
Other mistake: In some episode Ethel can play the piano and in others she cant.
Continuity mistake: In season 3, "Lucy and Ethel Buy the Same Dress", when Ethel comes out of her bedroom wearing the dress she had told Lucy she'd return, Fred calls her "Ethel Louise." In season 3, "The Million Dollar Idea", when Ricky tells Lucy and Ethel that it will cost them twenty cents to mail each dressing jar, Lucy takes Ethel by the hand and calls her "Ethel Roberta." In season 4, "Ethel's Hometown", throughout the episode Ethel is called "Ethel Mae."
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.
Lucy Thinks Ricky is Trying to Murder Her - S1-E1
Visible crew/equipment: When Ricky walks over to the table while he is on the phone with Jerry, a camera is briefly visible on the right hand side of the screen. (00:08:15)
Lucy Thinks Ricky is Trying to Murder Her - S1-E1
Visible crew/equipment: When Ricky and Lucy are dancing in the living room, the camera swings too far to the left, and the edge of the set wall and the adjoining bedroom set can be seen briefly.
The Girls Want To Go To the Nightclub - S1-E2
Visible crew/equipment: When Lucy and Ethel are talking about going to the Copacabana, just as Lucy leans toward Ethel before her remark about catching more flies with honey, the second camera/equipment can be seen at the right side of the screen. The same thing happens later, when Ricky laughs at the idea that Lucy and Ethel will have dates, as Ricky walks over to Fred standing at the desk, camera/equipment is visible at the bottom, right corner of the screen. (00:01:45)
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.
The Séance - S1-E7
Continuity mistake: After Lucy tells Mr. Merriweather that he's invited to the seance, when it cuts to Lucy unfolding the card table legs, note the couch behind her with one normal seat cushion on the left, but in the next wideshot there's an additional shorter cushion under the normal cushion. The small towel also repositions itself neatly on the couch. (00:11:55)
The Séance - S1-E7
Visible crew/equipment: After the first shot of Mr. Merriweather trying to contact Tilly on his ouija board, when it cuts to him answering the telephone we can see the moving shadow of the boom mic, on the door to the right.
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.
Revealing mistake: When Lucy is cutting up the fake fur coat to scare Ricky, it is clear that the parts that she has to remove are already cut and just loosely sewn in place.
Lucy Is Jealous of Girl Singer - S1-E11
Continuity mistake: When Ethel walks in while Lucy's vacuuming, Ethel has the folded newspaper under her arm and there's only small print on the paper, but after Lucy offers Ethel a cup of coffee now the headline can be seen on the still folded paper under Ethel's arm. Then, when Lucy unfolds the paper we see both the front and back page filled with pictures and the headline, but that area of small print which was seen in the earlier shots does not exist on either side. (00:00:40)
Lucy Is Jealous of Girl Singer - S1-E11
Visible crew/equipment: After Lucy goes into the bedroom with the newspaper and raises the window shades, when she walks around to Ricky's side of the bed, a crew member's shoulder/arm moves into the shot at the right side of the screen. (00:04:10)
Lucy Is Jealous of Girl Singer - S1-E11
Revealing mistake: During the rehearsal for the Jezebel number, the dancer's skirt trim is already partially torn or unattached to make it easier to tear, and it is clear that Ricky purposely steps on the trim to rip it off the skirt.
The Adagio - S1-E12
Character mistake: Lucy turns in for the night in full makeup and lipstick, instead of washing up.
The Adagio - S1-E12
Visible crew/equipment: Crew member shadow is visible at the foot of Ricky's bed near the end.
The Benefit - S1-E13
Visible crew/equipment: While Ricky and Fred are in the kitchen, when Ethel tells Lucy she needs her help getting Ricky for the club benefit, in the shots facing Lucy the shadow of crew/equipment movement is visible on the shutters to the right. (00:04:30)
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.