Frank Grimes states that Homer has the intelligence of a six year old.
This is also the highest rated episode of the series.
This is one of the few times at all that Homer actually was pleased about his Grammy (most of the time, he talks badly about the Grammys, such as in "The Mansion Family").
This is the highest rated Simpsons episode on IMDB, getting a 9.3/10.
Lenny and Carl have master's degrees, but Homer's degree, which he earned in "Homer Goes to College", is not mentioned; Homer did not complete a degree because Mr. Burns just had him take Nuclear Physics 101 to comply with the inspectors' requirement that Homer have college-level training in nuclear physics.
Homer shows Grimes his pictures and his Grammy, which reference numerous previous episodes:
As Lenny discusses how Homer didn't need a degree to get his job, his beard is drawn too low down for a frame.
A police auction would never let a piece of property go for one dollar. Realistically, the minimum bid would be much higher. Springfielders are not known for their intelligence.
When the sulphuric acid dissolves the wall, a piece of the wall is dissolved only to somehow appear again.
Bart removes two of the three safety signs on the staircase in the factory. Then, the third one vanishes on its own.
Lenny states that Homer started working at the plant on the day it opened. However, this is impossible since Homer applied for the job in 1980 in "I Married Marge", when the plant was already open (the plant opened in 1968 when Homer was twelve).
Marge says that she has five lobsters for the dinner with Frank Grimes. She should only need four, because Maggie is a baby and Lisa is a vegetarian. It is possible that Homer was planning on eating two lobsters, or that either Abe, Moe, or Mr. Burns was invited but did not show up.
The close up of Homer opening the door for Frank Grimes depicts a purple doorknob, but the next shot shows the doorknob as blue.
As Marge urges Homer to face his fear of Frank Grimes, the top of her hair is smooth and lacks the curls that it usually has.
Later in the same scene, the top of Marge's hair is drawn in front the top of the car's windshield, when it should be behind it since she is inside the car.
When Bart arrives at the factory after it falls over, Milhouse appears to be bald.
At one point, Sarah Wiggum is seen in the audience at the power plant model contest. Unusually, she is not wearing lipstick.
In a far shot of the audience at the power plant model contest, the lenses of Charlie's glasses are white instead of aqua.
For a frame, when Milhouse is trying to get coffee from the machine, the cup is drawn behind the platform which it is supposed to stand on.
When Lenny talks about his and Carl's degrees, his beard is off of his face for a frame.
Frank Grimes claims that Homer has never been fired from Springfield Nuclear Power Plant. However, he was fired in "Homer's Odyssey" (for crashing his tram into a stack of barrels) and "Burns Verkaufen der Kraftwerk" (when the German workers were laying off poor-performing workers -- with Homer being the only one on the list). Grimes was referring to the time in which he was a safety inspector, and in "Homer's Odyssey", he got fired before becoming a safety inspector. Plus, neither of those moments involved a meltdown or accident, which is what Grimes was pointing out.
Grimes says "D'oh" when imitating Homer. Homer never said "D'oh" in Grimes' presence. It is possible that Homer said "D'oh" in Grimes' presence off-screen.
During Frank Grimes' funeral, the Simpsons move from the second row of seats to the front row.
Also during the funeral, in a faraway shot Charlie's glasses aren't filled in so that they are just his skin color.
The poster for the Children's Design Your Own Power Plant Contest is behind Homer when he is in the break room. Later, Frank takes the poster and erase proof of it being for children. If it was behind Homer when he was in the break room, wouldn't he have not seen it and realize it was the actual poster without the evidence of it being for children? Homer's not very bright most of the time.
At the contest, Chief Wiggum is heard but not seen. Even if he was, he would be sitting next to his wife Sarah, who is seen in the audience. Hank Azaria adlibbed the line.
Frank receives his diploma in front of a home, but he lived in a single room on top of a bowling alley and below another. He may have lived somewhere else beforehand, possibly renting a house/room.