The gambler in the fez at the roulette table is the writer Bob Carroll, Jr.
Vivian Vance is in fancy clothes in this episode, just like Lucy. This is the beginning of Vivian demanding to have Ethel look more glamorous on the show, being tired of having to look frumpy. Vivian will get more leeway with her wardrobe and hair in the following season, but she won't have looking more glamorous in her actual contract until the start of The Lucy-Desi Comedy Hour.
The dress Lucy is wearing when she goes to Le Grille and wins the money is a dress she has on in a still commonly known as "glamour Lucy" in the merchandising world. This "glamour Lucy" same is the picture on Lucille Ball's commemorative stamp. Mattel also made a Lucy doll that was dressed in this outfit.
The restaurant in the casino that Lucy and Ethel ate at was called Le Grille.