1. Buffy the Vampire Slayer
Buffy is sorta the poster child for "Great TV show with a nigh-unwatchable first season." Pretty much all TV shows need to take a little time to work out the kinks, figure out what works and what doesn't, and find a good groove for the storytelling. But in 1997 WB, the stakes were a LOT lower than they are today - there were no Breaking Bads or Game of Thrones's back then, so TV shows could be given a little more leniency.
Still, Buffy season 1 is pretty terrible - but thankfully, it's only 13 episodes. Within those 13 episodes are great moments and great characters, much of which is the groundwork for what comes later, but there's also plots about hyena spirits possessing teenagers and making them eat their principal, a living wooden dummy (think Goosebumps) who's also a demon hunter, a demon borne of the Internet, and some really really regrettable things involving a praying mantis teacher.
Angel is a weird show - each season feels pretty weirdly distinct from the other, and it actually really only reaches its full potential in its final season, when Spike crosses over from Buffy on a permanent basis and Angel joins the bad guys (kinda). But what's definitely true is that its first season is kinda a mess.
The initial planned status quo for Angel - that the squad would be Angel, Cordelia, and an Irish dude who had 'visions' - only lasted for the first 9-ish episodes, when the Irish dude was killed off and replaced with Wesley Wyndam-Pryce. Still, the rest of Team Angel - Gunn, Lorne, and Fred - don't really come into play until season 2, when the show starts to actually become the semi-watchable Buffy spinoff it was destined to be.
3. Parks & Recreation
Parks & Rec pretty quickly grew into one of the funniest, sweetest, and most heartfelt comedies on the air - which is why revisiting the first season (cut short thankfully at 6 episodes) is so jarring. Leslie's a completely different character (basically a blonde Michael Scott), the show is much meaner to its characters, and it's just...not that funny, unless you're SUPER into Mark Brendanawicz.
4. The Office (U.S. version)
The Office started off on the exact wrong foot, trying to re-do the first episode of the British version of The Office, but with the new American cast and setting. And while it's a very funny script, the tone and rhythms of the American version are so different that the awkwardness overshadows a lot of the jokes.
On top of that, there were a lot of growing pains, with the writers and cast trying to figure out how to maintain what worked with the UK Office while also trying to create something fresh and new. The first season clearly showed signs of the greatness that would awaken, but were weighed down by a not-yet-fleshed out supporting cast (which soon became the show's secret weapon) and the sense that they still didn't know what this show WAS yet. Also, Michael Scott's slicked back hair is really, really weird.
Thankfully, this was another 6 episode season - so it's badness was short-lived. And really, you can dive straight into season 2 and not really miss anything (except - SPOILER! - Jim is pretty into that Pam girl).
5. American Dad
Seth Macfarlane has so thoroughly salted the soil of his work, that anything with his name associated with it tends to send a chill down the spine of anyone who comes in contact with it. And for good reason - Family Guy is a mishmash of completely random unrelated jokes and wild shifts in character behavior, The Cleveland Show is basically just a blander version of Family Guy, and that western movie he made was...well, I don't know. I didn't see it, because it looked pretty dumb.
But American Dad is actually GREAT. Like, not just great for something associated with Seth Macfarlane, but genuinely great on its own. The problem is that it began its life as something pretttttty legitimately terrible.
It's important to remember that it was created, in part, to fill the void for Macfarlane after Family Guy was initially cancelled after 3 seasons. It had a boorish husband, a hot wife, a nerdy son, and a butt-of-every-joke daughter, a megalomaniacal evil little harmless thing (a baby for Family Guy, a fish for American Dad), along with a faux-urbane thing-that-shouldn't-talk-but-does (a dog for Family Guy, an alien for American Dad). The main differentiator for American Dad was that it would tackle political issues - with father Stan taking the neoconservative perspective against his daughter Hailey's hyperliberal one. Needless to say, it plays like a less funny Family Guy that doesn't age well, due to its reliance on politics of the day.
But Family Guy WAS brought back, and it distracted Seth Macfarlane. While he still provided several key voices, he became basically completely uninvolved with the writing for the show, and by mid-season 2, the show was pretty great. By mid-season 3, the show had completely found its footing as one of the weirdest but well-written shows in primetime.
No one in this office believes me but I swear to god it's true. TELL THEM. TELL THEM ALL.