Other mistake: When Lucy responds to the money matter about her hair care, she states, "I can be a thin redhead or a fat brunette," when her real-life natural hair colour was blonde (later dyed to enhance her film career).
Suggested correction: Lucille Ball was naturally blonde. Lucy Ricardo was a brunette. This is, at best, trivia.

Revealing mistake: At Freddie Filmore's radio show, when Lucy steps out from behind the curtain, a bit of the kitchen from the Ricardo apartment is visible behind Lucy; it's the cabinet area with plates and canisters, beside the refrigerator. (00:06:15 - 00:19:40)
Lucy Has Her Eyes Examined - S3-E10
Other mistake: When the eye doctor has Lucy repeat the same letters on the eye chart that she claims Ricky got all wrong, she repeats the same letters out loud, then moves closer to the eye chart and repeats the same letters out loud, then pauses in error when she read them all off correctly: P E C F D.
Character mistake: After Ethel chooses the ladies who'll play instruments for their own orchestra, Fred enters the Ricardo apartment with muffs over his ears as off-key plucky piano is heard in the background, indicating Ethel is playing very badly, when in all prior episodes she played fluently for any of their show warm-up numbers.
Character mistake: Or continuity: When Ricky enters the Mertz's apartment, waking everyone up, little Ricky starts crying in the crib, and Ricky moves closer and accidentally says, 'Why is she awake?' instead of 'he,' as his own baby daughter Lucie was almost 2 at the time.
Suggested correction: The issue was due to his accent; several times during the course of the show, when Rickey said "he," it sounded like "she."
Revealing mistake: The scenery 'lines' are quite visible on the backdrop as Ricky practices his swing, with Fred indicating this was shot in-studio.
Equal Rights - S3-E3
Factual error: While dining out, Ricky proceeds to shave with his electric razor plugged in on the floor by the table. Purely a studio convenience, not reality; strictly for laughs.
Other mistake: When Lucy tosses the umbrella off the balcony during the Mexican serenade, Ricky somehow doesn't appear to hear it hitting the floor during the pause and keeps on singing. (00:23:30)