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 is 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.
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 1960s.
Principal Wartz asks Grandpa, "Young man, are you looking for trouble?" to which he replies "Maybe, Whadda ya got?". This is in reference to the 1953 movie The Wild One.
The story itself is similar to the 1995 movie "Billy Madison" in which a man has to retake elementary school to claim his family fortune.
Grandpa claims that the biggest export of Minnesota is Bob Dylan, who is from Duluth, Minnesota.
"Melts in your mouth, not in your hand" is the old slogan of M&M's.
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.
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. This is only true if the isosceles triangle is also an equilateral triangle; technically, he should have used "equilateral" instead of "isosceles."
Harold laughs, despite him being held back several years too.