
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: While Lucy and Ethel are at their charm school, when they're standing in front of Miss Emerson's desk, in the widehots a small tape mark is visible on the floor in front of Lucy's feet. Then, when Lucy and Ethel are in sweatpants there are two small tape marks on the floor, and when Ethel walks to the other side of the room to join Lucy, there's another tape mark which Vivian even looks down at to confirm her foot's position.

Visible crew/equipment: When the chicks are running loose in the living room, and Lucy, Little Ricky, Fred and Ethel are trying to corral them, you can see the chicken wire and braces set up to keep the chickens on the set. (00:20:20)

Ricky and Fred Are TV Fans - S2-E31
Visible crew/equipment: When Lucy decides to use the scissors to cut the TV wire on the roof, she and Ethel walk out of the kitchen, and at the start of the next shot we can see the end of the set wall and black cables on the floor, at the right side of the screen.

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.

Visible crew/equipment: When Ricky is with John Wayne in his dressing room at the studio, getting yet another set of footprints on the block of cement, three T-marks are visible on the floor. One of those T-marks can be seen closeup when Wayne is lying on the table for his rubdown. (00:18:10)
Visible crew/equipment: At the start, when Lucy pulls into the "gas station" the thin cable pulling the Pontiac is visible in front of the car, and when Ethel walks in front of the car note that the actress quickly glances down and steps over it, just as she says they're lost. Additionally, the glass windshield and rearview mirror are gone.

First Stop - S4-E14
Visible crew/equipment: While Lucy and Ricky are lying in the sagging mattress "canoe", when the train passes and their bed rolls towards the bunk bed, the end of the set wall is visible at the right side of the screen. (00:17:30)
California, Here We Come! - S4-E13
Visible crew/equipment: When they're all finally in the Pontiac ready to leave NYC, just as Ricky starts to drive away we can see cables jiggling under the Pontiac, to the left of the front tire, pulling the car. Funny to see how Ricky puts his hand on the gear stick, but never actually does anything with it. (00:23:40)

Visible crew/equipment: While Ricky and Fred are trying to clean up the volcanic rice eruption, when Ricky slips on the floor the second time the front edge of the raised kitchen set's platform can be seen. (00:19:15)

Visible crew/equipment: During the scenes at the small diner when it's open for business, such as when Marco walks in, there are two small chalk T-marks on the floor in the area near the door. The T-marks are also visible when Ethel and Fred walk back inside. (00:12:35)

Bonus Bucks - S3-E20
Visible crew/equipment: After Ricky sneaks the dollar bill into Lucy's purse he sees her stirring in bed, and when Ricky ducks down to hide from Lucy, the two curved chalk actor's marks are visible on the carpet. (00:07:15)

Visible crew/equipment: When Ethel's on the stoop in front of the building waiting for Lucy and Ricky, right before Ethel asks Ricky about Lucy's driving lesson, just as Ricky drives up we can see cables moving in front of the new Pontiac pulling the car. Then, when Ethel crashes the new Pontiac into the old car, the jiggling cables are again in front of the new car. Lastly, when Lucy finally starts the old car's engine, now there's a moving cable in front of the old car as well. (00:09:50)
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)
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)
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)
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.
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: After Lucy and Mr. Beecher sign the lease, just as they all start heading toward the door, the taped T-mark is visible at the bottom of the screen at the edge of the carpet (presumably for the second camera dolly offscreen at the left). Then as Mrs. Hammond walks out, a bit of overhead set equipment can be seen at the top right side of the screen. (00:12:45)
Visible crew/equipment: After take one of Ricky's Screen Test, when the director says to Lucy, "I thought it might add interest to the scene if you could make it go around and around like a lighthouse!", the Ricardo's kitchen cupboards and fridge are visible off stage to the left of the director's head.
Answer: There is no reason. It's a just a silly plot device, typical of the era. Women characters were often portrayed as making uninformed assumptions or decisions.
raywest ★