The trailer from the movie was made in Alma, Michigan. One woman, who made the curtains for the movie, received a piece of the set, the round table that folds. It is still in the family as an heirloom.
The New Moon trailers, produced by The Redman Trailer Co. (as per original sales brochures & in viewing the actual 1953 models), didn't come with a "sunken living room" as was highlighted in the film. This was done to add a reason for Desi Arnaz's character to take his pratfall when first entering the trailer. You can see that the floor of the kitchen is flat with the living room floor if you look closely when he opens the door for the first time at the trailer show, as this was simply a regular production coach in the shot. The interior shots had a "dropped" section in the living room area and you can see that the vent windows are much further from the ceiling than they would be as seen from the exterior. New Moon trailers also had a furnace in the corner between the front door and the kitchen cabinet. It is assumed this was removed from the interior mock up for aesthetic reasons.
When Nicky and Tacy are at the service station after being pulled out of the mud there is a Phillip Morris sign on the front of the station. Phillip Morris was the sponsor of "I Love Lucy" at the time.
In the original cut of the film, the "Breezin' Along with Breeze" musical number had an entirely different backing track orchestration. However, director Vincente Minnelli did not approve of the final cut, and removed the music from the sequence, leaving only the original vocal overdubs, in which he then ordered an entirely new orchestral number, and mixed the vocals within the scene. The original recording, however, was thought to be lost forever, until recently resurrected from the MGM vaults and compiled onto a love songs CD by Rhino Music.
The chorus of the song "Everything Right is Wrong Again" by the band They Might Be Giants references the scene where Lucy's character is stuck in the trailer which has become unhinged from the car. "Everything right is wrong again Just like in the long long trailer All the dishes got broken and the car kept driving And nobody would stop to save her"