These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fanon Discontinuity: Many fans refuse to acknowledge the existence of the eighth season and prefer the cut-off to be somewhere mid seventh season.
Fan-Preferred Couple Hyde/Jackie, which is also a subversion; the two were together for a large chunk of the series (about 3 seasons), but officially ended in season seven after some other temporary break ups.
Eric wearing an all-black outfit wishing he could shoot webs and later saying he learned how to fight from Spider-Man. Topher Grace went on to play Venom in Spider-Man 3, who had all of Spidey's powers, wore a symbiote that was black as a costume, and could shoot webs.
In "Going To California," Hyde tells Eric that he "has no problem fooling whitey." Eric reminds Hyde that he's white, and Hyde responds by saying, "Barely." Cut to Season 7, where it is revealed that Hyde is half-black.
All of Jackie's lines are funnier when you picture her as Meg Griffin (who, like Jackie, is a Butt Monkey, though Meg's abuse does cross the line to Dude, Not Funny! territory, while Jackie's humiliations are more light-hearted).
Donna once said "I could get arrested. I could go to a girl prison". Cut to 2013...
Ho Yay: There was an episode where a Eric became friends with a guy called Buddy (played by Joseph Gordon-Levitt). There was a montage of them hanging out to a Best Friends song, only for it to turn out that Eric's friend was gay. At the end of the episode, Red and Bob had a Best Friends montage.
Ship Tease: Jackie/Hyde had there fair share of teasing in the early seasons whenever she broke up with Kelso. Both couples actually came to fruition over the course of the series.
Strangled by the Red String: Donna and Randy. Donna is noticeably attracted to Randy while she's still in a relationship with Eric. The fact that the writers also broke up the Official Couple (and having it be an off-screen Eric's fault, no less) just to get them together doesn't help.
Strawman Has a Point: After getting Brooke pregnant, Kelso is initially reluctant to get involved or take responsibility, which leads to the others criticizing him. While they're certainly not wrong, Kelso has a pretty understandable response: "Y'know, it's real easy to talk about the right thing when it's not your life."
The season five episode "Nobody's Fault But Mine (Hyde Loves Jackie)." In the last episode, he saw Kelso and Jackie together and thought she was cheating; as payback, he cheats with a nurse he just met. After Kelso explains to Hyde that nothing happened, Hyde and Jackie have a talk. Unfortunately...
Hyde: Come on, Jackie...
Jackie: No, you know what, Steven? I'm sorry... it's over.
And also from the same episode, particularly this dialogue:
Hyde: Jackie, I love you.
Jackie: Yeah, well I don't love you.
In the final episode, the Eric/Donna montage (set to Big Star's "Thirteen") followed by his appearing to wish her Happy New Year and apologize for having left her.
Kelso, being The Ditz, is naturally a fountain of this.
One of the group's favorite stories is of the time Kelso tried to do the "burning bag of dog poop" prank on someone, but lit the bag prematurely and then stomped it out himself. A frustrated Kelso counters "THE BAG WAS ON FIRE!"
Eric more or less invokes the Idiot Ball in "The Good Son," when he tries to lash out by doing something stupid and allows Kelso of all people to persuade him to bounce a bowling ball off the couch. However, the idea turns out to be even dumber than he thought, as the ball ends up bouncing into the TV. Not many viewers are sympathizing with Eric's Oh, Crap face at this point.