When Mary answers the radio, it's an inside joke, as the voice on the other end - who's asking for 'Fred', is Harry Corden, a noted voice-over actor, and amongst his best-known roles were as 'Fred Flintstone', and (at the time of filming his episode, he was) 'Charlie - the Tuna'
James Brooks, who wrote this episode, also wrote Christmas and the Hard Luck Kid, an episode of That Girl. There is no apparent connection between the two, other than Brooks.
Literary allusion: When talking about spending Christmas Eve alone, Rhoda asks if she's supposed to stand out in the snow and light matches. She alludes to "The Little Match Girl", a story by Hans Christian Andersen.
This takes place in December 1970.
Lou gives Mary a blank check in her Christmas card. On the Dick Van Dyke Show Rob and Laura give a blank check in the "I'm No Henry Waldon" episode.