Bart writes on wall "Skinner is a wiener" ("Bart the Genius"), he says that is the first time after 30 years. However, "Bart the Genius" was aired in 1990,
Homer shaved his beard, giving him a very smooth face. Seconds later, he went to show Marge his new face, only for his beard to be back on his face again almost immediately afterwards. This is continuity on a gag used in the episode ("Some Enchanted Evening"), where when Homer was getting ready for his date with Marge, he shaved his beard and it immediately grew right back on his face again. This pretty much makes this beard thing an official trait about Homer Simpson.
In the middle of the episode the trio (Carol, Bart and Skinner) are in the playground and Skinner calls her Herrera, not Berrera. This is not only in the audio track but the captions on hulu also spell it with an "H" this one and only time on the episode (each and every other incident spells it with a "B").