The windshield of the 1955 Pontiac convertible was removed to avoid studio light reflections that would ruin takes.
When Lucy wants to teach Ethel how to drive, Ethel says "Pardon me, Barney Oldfield." Berna Eli "Barney" Oldfield was an American pioneer automobile racer; his "name was synonymous with speed in the first two decades of the 20th century"
The 1923 Cadillac and 1955 Pontiac seen in this episode are probably the biggest "props" used in the Lucy series. As they were shooting on a sound stage, actually driving the cars was not feasible, so they moved the vehicles on and off with cables. The Pontiac's cable can be seen clearly in the shot where Ethel is driving and she rams the back of the Cadillac. The cable can be seen again as Lucy drives off in the Cadillac (with the Pontiac stuck in back) to get the cars repaired; and once more when Lucy returns driving the Pontiac (with the Cadillac stuck in back).
When Lucy goes 'catatonic' in the last scene, a fly makes a conspicuous landing on top of her hair.
When Ethel rams the Cadillac with the Pontiac, there is a slight hesitation before the headlight bezel flies off the Pontiac.