The title is an obvious reference to That '70s Show, and also to the short-lived That '80s Show. Like The Simpsons, both aired on FOX.
Sadgasm parodies Nirvana, a Grunge band whose songs are parodied by the band. Homer even occasionally wears the T-shirt Kurt Cobain wore in the music video for "Smells Like Teen Spirit". (The green striped t-shirt with long white sleeves.)
"Weird Al" parodies Homer's song "Shave Me" (Titled "Brain Freeze"), a parody of "Rape Me" by Nirvana, which harkens back to his actual parody of Nirvana's "Smells Like Teen Spirit".
Sadgasm's first song "Politically Incorrect" is a parody of two of Nirvana's songs combined "Heart Shaped Box" and "Frances Farmer Will Have Her Revenge On Seattle".
The episode also made references to Sonic the Hedgehog, Zima, Seinfeld, Melrose Place, and Comic Book Guy mentions that The Lord of the Rings could never be filmed (although an animated film adaptation was produced in 1978).
Homer's song "Margerine" is a parody of "Glycerine" by Bush.
The scene where "Marvin Cobain" calls his cousin Kurt to tell him about the new sound he's "been looking for" is a parody of the scene in Back to the Future where "Marvin Berry" makes a similar call to his cousin Chuck.
This episode conflicts with other 'flashback' episodes. Past 'flashback' episodes feature Homer and Marge in their twenties/ early thirties during the eighties and early nineties and already had Bart, Lisa and even Maggie. This is due to the Floating Timeline that prevents anyone in the Simpsons from aging with no suitable reason as to why.
It was also mentioned in this episode that Homer and Marge went to Springfield University together, despite the fact that not only did Homer not graduate from High School, and not even be accepted into College due to fighting a dog over a piece of ham, but he wasn't even assigned to Springfield University until after Mr. Burns arranged for him to be accepted when Homer's previous applications were rejected.
We learn Homer had diabetes at one point, from drinking too much Frappuccinos, and that the syringes he had weren't heroin, but insulin doses.
The timeline for this episode is questionable. Young Homer references "The Sponge" episode of Seinfeld, which originally aired in December, 1995. Which would set these events after that. However, "Marvin Cobain" calls his cousin, Kurt, upon hearing Sadgasm (suggesting that Kurt was inspired by Sadgasm), which would in fact require this story to be set pre-1987 (when Cobain's band, Nirvana, started). Furthermore, Cobain killed himself in April, 1994. Making a setting in late 1995/early 1996 (which would be required for the younger Homer and Marge to be able to reference "The Sponge" and "The Soup Nazi", which were both aired in late 1995), impossible.
In reality Bart, Lisa, and Maggie have been in the 90's since they were born in the 80's and early 1990s (Bart was born in 1980, Lisa was born in 1982, and Maggie was born sometime in 1989).