According to series creator, Carl Reiner, leading actress, Mary Tyler Moore was in progress of completely quitting her heavy cigarette smoking habit as this program was being filmed in February & March of 1965. She was therefore extremely stressed out and walked off the set in protest over her lack of actual screen time in this episode. Most of the character's time would be spent off screen in the hotel bathroom. Reiner placated Moore and she returned to the set, later admitting how humorous the episode turned out to be.
Millie says that the Petrie's minister is named Charles Brown. That was the name of Dick Van Dyke's real life minister at the time.
The shooting of this is famous for 1) being the only time Carl Reiner ever lost his temper on set, and 2) the first and only time one of the show's stars walked off the set and left the studio. Mary Tyler Moore had been trying to quit smoking, so she was more dealing with withdrawal than anything else, and she was also upset that her character would be offscreen most of the time.
Rob drew on the mustache so he would resemble the suave leading man, David Niven. Millie tells him he looks like Ben Turpin. The latter star was a silent movie comedian with crossed eyes.
Kathleen Freeman appeared twice on The Dick Van Dyke Show (1961). The first time was in Honeymoons Are for the Lucky (1964) where she played the owner of the hotel Rob and Laura had their honeymoon in. The second time was in Never Bathe on Saturday (1965), where she played the maid at the hotel where Dick and Laura had their second honeymoon.