In the episode where Mary had her tonsils removed, originally she was going to have a tattoo removed. Ms Moore in real life refused saying she was a "good catholic girl" and she "couldn't play that," so they changed it to a tonsillectomy.
I'll trade you my B for your "Where are we going tonight?"
Exteriors of Mary's residence show that the apartment with the balcony (which would be Mary's, based on the interior shots of her apartment) is on the top floor, yet Rhoda's apartment is upstairs from Mary's. However, Rhoda's apartment is located in the attic of the building.
This series introduced the MTM Productions logo at the end - a tiny, meowing kitten. This is a parody of the MGM Studios roaring lion. The kitten logo (or variations thereof) would be used throughout the 1970s and 80s on a number of different TV series.