Homer is disappointed with the Denver Broncos, even though in "Cape Feare" he said he wanted his alias to be John Elway (who played for the Broncos at the time that episode debuted), before expressing disappointment that the Witness Protection Program chose the new name for him.
The Denver Broncos were not a good team at the time (hence Homer's disappointment in owning them), but would ironically win two consecutive Super Bowl championships after the airing of this episode.
Homer buys Tom Landry's hat in this episode. In later episodes such as "Bart Star", where he also leads a team, he is seen wearing it.
When Hank Scorpio describes where to get hammocks, he was talking to the extent that Homer couldn't follow until he caught up with him and replying "Oh, in the Hammock District." This was because their voice actors had similar actions during the recording of the scene: Al Brooks, the one who voiced Hank Scorpio, was ad-libbing throughout the entire scene, causing Dan Castellaneta, Homer's voice actor, to be unable to follow.
In the original scene in which Homer asks Hank Scorpio for sugar, Hank asks Homer, "Want some cream, too?" This was omitted in syndication.
This is the second time a joke is made about Bart mistaking cursive writing for profanity (the first is the blackboard gag on "Bart's Comet" that reads, "Cursive writing does not mean what I think it does.")
One of the items that Ned Flanders asks if Homer is still using is his TV Tray, an item of which Ned loaned to Homer when Lisa was born as seen in the episode "Lisa's First Word".
Homer has worked at the Springfield Nuclear Power Plant for ten years. This supports "I Married Marge" as Bart is ten years old and he has been working there since Bart was born.
It's implied that most of the kids in the One Leg Up program aren't really slow. Bart was placed in it because he never learned to read cursive and his new teacher thinks he can't read. Another boy is in it because he starts fires. A girl in the class says that she hit her head after falling off the jungle gym and when she woke up she was in the class.
Homer states to his disappointed family that "(..) and for the first time in my life, I'm actually good at my job". But he did good as a pin monkey at the bowling alley in "And Maggie Makes Three" too.