In another episode it was established they lived in another city, with Lisa and Maggie not having been born yet, so they were not yet living in Springfield and it's not likely Dr. Hibbert was the doctor they saw. And therefore Homer wouldn't be working at that plant of be able to see it from the window.
When Homer is writing his goodbye-letter to Marge he completely scratches out Patty's name on the paper. In the next scene it has just a line through it.
During the final part of Homer's speech about he and Marge being blessed with three children, Maggie's ribbon briefly disappears between shots.
Homer scratches Patty's name off the stationary and writes his name directly below hers and horizontally, but when Marge is reading the letter, his name is slightly to the right and diagonal.
When Homer and Marge exit the movie theater, having seen the Empire Strikes Back, the Imperial March (Darth Vader's theme music) can be heard playing. The Imperial March does not play in the end credits music until about half way through the credits roll. Presumably, they left the theater when the credits began; the music would not begin until later in the sequence.