While they are talking about Dore Schary, Mrs. MacGillicuddy keeps asking who he is, even though earlier when Lucy and the gang are planning their trip to California in ("California, Here We Come!" - Season 4, Episode 12), Mrs. MacGillicuddy mentions that she plans on showing Dore Schary her book about her family.
In the last scene as Dore Schary is saying goodbye, the shadow of a stagehand can been seen in the small high window. From behind the set, you can see someone carrying a long pole from one side of the set to another.