During Homer's first bowling game (where he bowls a perfect game), Homer is upset that Lenny and Carl are using the names "ASS" and "POO." Resulting in Homer instead using "HJS" (his initials). This seems to indicate that when choosing a name on the scoreboard at the bowling alley, only three letters are allowed. However, at the end of the episode, when he bowls with Maggie, their names on the scoreboard read "DADDY" and "MAGGIE." Now indicating that up to six letters can be used.
When in the ocean, Homer's goes from wearing shoes to not wearing shoes several times throughout the scene.
When Homer is punished by Mr. Burns he is forced to eat "all these drums of toxic waste." Carl replies, "Geez, that's rough. There must be 200, 300 gallons in here!" In fact, there appear to be nearly 30 drums visible in the room (with more behind each visible stack). Assuming they are standard 50 gallon drums, that is well over Carl's estimate. Bon appetit Homer.
Surprisingly, Mr. Burns recognizes Homer and doesn't need Smithers to remind him who he is or that he works for him. In addition, he is unusually strong. Now able to restrain and beat up Homer.