"Funny Aneurysm" Moment: Many, many sketches involving psychiatrists or institutionalization can seem a bit disturbing in light of Fry's mental problems in The '90s, as well as the later diagnosis of the pair's mental illnesses (Fry has bipolar disorder, while Laurie has severe clinical depression).
A sketch in the first season has Fry deliver a throwaway line that he's no judge of poetry because "I'm an English professor, not a homosexual". As of 1995, he is out as a homosexual, which turns what was once a racy and potentially offensive joke into a case of N-Word Privileges.
The "information" sketch. It's a sketch about the World Wide Web. From 1989. Even more amusingly, Stephen Fry character plays an apparently search-engine-like entity - a few years later, his Jeeves character would turn up as the logo of a real-life search engine.
Ho Yay: The sketch "Judge Not" strongly implies that the judge is gay, and the lawyer's also attracted to him. Since a lot of it's apparently parodying homophobia, that's not surprising.
Tear Jerker: "How do I like it? I like it the way Tony Murchison used to make it." *sniff*
The Woobie: One first-season sketch sees Laurie as a university teacher who can't elicit any reaction from his students. Any reaction at all—every single question, suggestion, etc. that he poses to the class is met with an icy indifference, with the students' only statement coming in the form of a message written on the chalkboard at the outset: "You barstad [sic]". Throughout it all, Laurie maintains a faltering, overly eager Stepford Smiler act, praising the students for their tacitly negative responses to his questions and berating himself for leading the class astray with trivial theories. It's such a woobie role that when the professor finally sees himself out, Laurie was aww'd off set by the pitying audience.