Factual error: When Homer and Candy go to the movies, the theater has stadium seating. This seating style in theaters wasn't used until much later, not in the early 1940's, and certainly not in Maine.
Continuity mistake: When the couple is parked at a drive-in cinema and watching a dark screen because of a blackout during World War 2, the shape of the screen is that for widescreen or Cinemascope movies, not common until about 10 years later.
Revealing mistake: When Homer is sitting outside (on a dock?) reading a letter from Dr. Larch you can see through the envelope and the letter because the white paper is thin. You can tell there are writings on the letter but it is equally obvious that the envelope is blank with no address written on it.