The girl in the park who thinks Kermit is a bear is Christine Nelson, daughter of Muppeteer Jerry Nelson (with whom she appears in the scene). Christine suffered from cystic fibrosis throughout her short life, and finally succumbed to the disease in 1982, one year after the film debuted.
The end of the bicycle scene (where all the Muppets are shown riding together) was actually done by putting all of the Muppet characters onto their bikes, hooking them together, and pulling them. Brian Henson, on an oversized tricycle, was among those who pulled the bikes.
Miss Piggy's underwater musical number was the most difficult scene to shoot, mostly because of communication problems. Lighting, cameramen, cameras, speakers, and monitors were all underwater. There were also 18 professional swimmers who had to dive into the pool at the same moment. In the June 1981 issue of the children's magazine Dynamic, director Frank Oz said, "The water ballet scene with Miss Piggy was really wonderful. I was under the water for a week. I had three days of scuba training and then down I went. Having them swim for the first time really was exciting!"
Nicky is connected with a running gag of wearing flowered socks, the first reference being when they are delivered to his office and the second and third being quick shots of his ankle during the supper club scene and later during the heist of the baseball diamond. During the fashion show, the only scene without a shot of his flowered socks, he is wearing a matching flowered bow tie and handkerchief.
Another running gag is the subtle repetition of the exact phrase, "the fabulous baseball diamond." Lady Holiday is the first to use the phrase, followed by the reporter after Miss Piggy's arrest, then Lady Holiday repeats the phrase back to the reporter, and finally by Kermit during the heist.