The numerous times Calvin & and the others spork movies that are proclaimed to be pretty pathetic in-universe, it seems quite a bit like Mystery Science Theatre 3000. They even make multiple references to it in other parts of the show.
'The Spirit Room' has the gang dressing up as the various Doctors for Halloween, with Calvin being the 7th, Hobbes being the 4th, Andy being the 5th, Sherman being the 3rd, and Socrates being the 6th. Seems to reflect their personalities a bit.
Hobbes: Whoa. I haven't seen such fashion disasters since John Nathan-Turnernote the producer of Doctor Who from 1980 to 1989 thought question marks were fashionable. Calvin: Well, fair play to the actors. Not a lot of men can make punctuation look decorative.
Socrates: Well, obviously you'll need me for this! I mean, who else could possibly keep this young man out of trouble and do a better job than me? Calvin: I dunno... Alec Baldwin?
Andy: And people wonder why our landfills are full. Socrates: Really? Then it's my duty as a citizen of This Island Earth to make up for that! To the midway!note This is probably more of a reference to the Mystery Science Theater 3000' movie, which riffed This Island Earth.
Calvin whistles the Doctor Who theme near the end of "Dark Laughter Part 2".
Sherman gets concerned about a worldwide helium shortage thanks to The Daily Show.
Subverted in the author's notes in "Temporal Delay" - it was originally named "Terror From the Year 2011", then "2012" (a reference to Terror from the Year 5000, another movie featured on Mystery Science Theater 3000), but was changed to its current title for two reasons: the title would've been dated and there isn't really a "terror" in the episode itself.
One of "Black Rain"'s plotlines concerns Socrates getting stalked by the Slender Man, and he later freaks out about seeing a guy in a mask and hoodie (who is later revealed to have a knife) - something rather similar to the Marble Hornets character Masky. (It's worth noting that Swing 123's YouTube account is subscribed to the series' channel.)
Part 4 has the group watching an old VHS, and its contents are a dead-on representation of one of totheark's videos (horrible screeching, shaky footage of forests, strangely punctuated words, and the Operator symbol everywhere).