Danny Thomas, Marlo Thomas's real-life father, appears as himself, but unrelated to Ann. In an earlier season, he appeared as another father of sorts, also unrelated to Ann. In My Sister's Keeper (1969) he appears as a priest.
Two special guests play themselves, Milton Berle and Danny Thomas. This adds them to a short list of celebrities who played themselves on the show, which includes Ethel Merman and Stan Musial.
Marlo Thomas is the daughter of Danny Thomas, who appeared in this episode.
When Ann is on stage with Milton Berle and kneads his mouth in her hand in an attempt to instruct him on proper pronunciation, she is appropriating and performing the same shtick that he often performed on others.