This episode features an inordinate amount of jokes involving male genitalia, ie, the circus performer thrusting his crotch in Homer's face, Wiggum ostensibly urinating in the snow, Willie saying "that's the last time you'll slap your willie around", the ranch dressing hose, Skinner saying "chew through my ball sack", and a particular shot of the salt silo sliding down the hill (where the arrowhead like peak inexplicably becomes round and bulbous).
Bart's permanent record reads "underachiever and proud of it," to which Bart disdainfully says "how old is this?" That phrase was used to describe Bart's character during voice auditions back when the Simpsons were part of 'The Tracey Ullman Show' (indeed, it's what inspired Nancy Cartwright to read for Bart instead of Lisa, as she had initially been meant to).
In the original airing, the permanent record page that Milhouse rips out of Lisa's permanent record uncrumples and reattaches itself to her record and causes the shelves to slam shut. It is later cut from broadcast for time.
Skinner's furious reaction to Groundskeeper Willie's reluctance to destroy the tunnel Bart dug ("well, I see your Scotsmen are thrifty with courage too!") is based on an ugly stereotype commonly referenced in Europe about how Scottish people are cheap and go out of their way not to spend money if they can avoid it.
Bart's chalkboard gag: Science class should not end in tragedy.