Ricky claims to have gotten tickets for the opening night of a new Rodgers and Hammerstein show. Although "South Pacific" and "The King and I" were still playing on Broadway at the time the show was filmed and aired, there was no new Rodgers and Hammerstein show until "Me and Juliet" in May 1953.
When Ricky enters the bedroom near the end to see Lucy and Ethyl's handiwork, Fred can be seen in the doorway waiting for his cue. He steps back out of frame after Ricky and Lucy enter.
Although Lucy had signed a bill of sale, Mr. Jenkins never paid her the $75 for his purchase of the furniture. Having not completed his end of the contract, he still did not legally own the furniture when he sold it back to Ricky. (Not a plot hole. In a scene on the DVD that is perhaps cut from syndication prints, Jenkins paid Lucy $75, peeling bills off a wad of cash. It was that cash that Lucy used to buy the wallpaper and supplies.)