This episode's story was likely conceived much earlier in the show's production run, as it credits Joe Ansolabehere, who left after Season 1.
Arnold's homework problem is 325 divided by 27.6. Unless Arnold was told to round off to a certain number of decimal places, as the answer is 11.77536231884057971014492.
Oskar and Suzie sit on opposite sides of the table in the scene where Grandpa tells everybody he's been promoted to sixth grade, possibly indicating that they have been fighting again.
This is the second time voice actor Dan Castellaneta has said the line, "The sum of the square root of any two sides of an isosceles triangle is equal to the square root of the remaining side" in a TV series. The other time was when he voiced Homer Simpson in The Simpsons. It’s a line originally spoken by the Scarecrow in the classic 1939 film The Wizard of Oz. No matter who says it, this statement, supposedly attempting to refer to the Pythagorean theorem, is mathematically incorrect.
This and its' paired episode "Egg Story" both premiered on Nickelodeon the same day Looney Tunes on Nickelodeon had its final run on the network.
Phil Shortman pulls the fire alarm, which is something that Eugene has been accused of in the episode False Alarm
Cultural References
When Arnold states that Grandpa has plenty of brain cells, he replies, "No, not since Woodstock." This is a reference to the drug use during the Hippie movement of the 1960’s.
Principal Wartz asks Grandpa, "Young man, are you looking for trouble?" to which he replies "Maybe, Whadda ya got?". This is a reference to the 1953 movie The Wild One.
The story itself is a reference to the 1995 movie Billy Madison in which a man has to go back to elementary school to claim his family fortune.
Grandpa initially claimed, moments before realizing his mistake, that the biggest export of Minnesota is Bob Dylan. The joke is that Bob Dylan is from Duluth, Minnesota.
"Melts in your mouth, not in your hand" is the old slogan of M&M's.
Grandpa stated that "The sum of the square root of any two sides of an isosceles triangle is equal to the square root of the remaining side," which is not always true but is a reference to the same 'error' made in the 1939 film The Wizard of Oz.
Recall that Craig Bartlett's brother-in-law is Matt Groening, the creator of The Simpsons. In an episode of The Simpsons, "Homerland", Bart says the same thing and explicitly refers to The Wizard of Oz.
Homer also says something similar in the episode "$pringfield".
Continuity
Harold laughs, despite him being held back several years, too, as he mentions to Patty at Rhonda's party in "Hey Harold!".
Errors
When Arnold was quizzing Grandpa, he asked him the capital of Minnesota. Grandpa answered Duluth, which is incorrect; the capital of Minnesota is St. Paul.