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.
Other mistake: Lucy walks out on the balcony and sees Van Johnson sleeping on a lounge chair by the swimming pool. The photographic backdrop shows automobiles, trees, mountains, the Roosevelt hotel and many other buildings of Hollywood but when Lucy goes to the pool and sits on the lounge chair next to Van Johnson, the background is just a plain painted backdrop with no cars, trees, mountains or buildings. This plain backdrop also appears in the episode with Harpo Marx.
First Stop - S4-E14
Other mistake: When the Ricardos and Mertzes arrive the first time at One Oak Cabins and Cafe the full moon is amid the tops of the trees. When they arrive the second time the full moon is in exactly the same location amid the tree tops as the first time they arrived. Fortunately, hours later when they make their sneaky escape from the cabin and return to their car the moon is no longer in view.