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.
Anvilicious: Like a lot of 80s cartoon series, a lot of this show's episodes were focused on some specific "moral", and weren't very subtle about it.
Somewhat justified in that Lion-O needed to be taught these lessons and quickly so he could become an effective leader.
Ass Pull: Some characters (including Lion-O) somehow get massive powers on convenient moments, like Cheetara's psychic Limit Break.
Bizarro Episode: Most of the William Overgard episodes tend to be this. One episode had Lion-O go to another planet without the Sword of Omens, defeat the Lunatacks with common household products, and then he was able to summon the sword from all across the galaxy to the planet he was on and flew back to Third Earth with it.
Tygra also garnered some decent popularity, especially with girls watching the show. He was the Thundercat besides Lion-O to get a new figure in Bandai's line of classic ThunderCats. Many of his fans were upset by the changes made to his personality in the 2011 reboot.
Pumyra was under-utilized because the producers often didn't know just what to do with her, but many fans claim her as their favorite character. The anticipation surrounding her appearance in the 2011 reboot is insane.
Grune was one of the more popular villains despite a handful of appearances.
Alluro was pretty well-liked even by fans who hated the season 2 cast additions.
As creepy as Mumm-Ra was, the Living Ooze was definitely the scariest thing on the show.
A nightmare-tastic episode has Lion-O was trapped in some creepy catacombs with these Morlock-esque creepers with gigantic eyes, speaking about how they had been driven out of the world by people being too terrified of what was written in their books.
Since they're supposed to be "normal" where they come from, Alien Scrappy also.
Special mention should go to Snarfer, who was just downright annoying. Also the three new ThunderCats from season 2 weren't very well-received.
Judging by the new animated trailer, they may be attempting to rescue Snarf from the Scrappy heap. They were actually able to do this by changing the Snarf race into a species that doesn't talk.
The character probably most deserving of fans' hatred is Captain Bragg, who made the Mutants and Lunatacs look like a bunch of chumps and put them on a train out of the series. He gets away with hypnotizing WilyKat and tricking him into helping him and doesn't get punished for it. Bragg doesn't even have any real coolness to him to make up for it, he's just an old circus ringleader with a talking crow.
Weirdly enough, Tygra of all characters was apparently this to the original series head writer Peter Lawrence, who considered Tygra "boring" (and because of it Lawrence reportedly shipped Cheetara with Lion-O rather than Tygra). Lawrence didn't think too highly of Pumyra either, which is why they both got Put on a Bus (or rather left behind) in the fourth and final season (with Tygra's final appearance forcing him to carry the Idiot Ball).
Mumm-Ra sets up a plan to lure Lion-O to an area where his most formidable opponents will be waiting for him. Summoning Slythe, Safari Joe, Spidera, and (just to make sure) Ratar-O, it was explicitly stated that Lion-O was to face them combined as each gave him a hard time in the past so there was no way he could conquer them all at once. He only ends up fighting two of them, and separately no less.
"Telepathy Beam" has Cheetara receiving a startling vision of the Mutants making short work of the Berbil village with more brutality than seen before and then Skytomb itself arrives on the scene. So disturbed is Cheetara witnessing their plight that Lion-O vows to settle things once and for all. The whole thing turned out to be a false alarm which suited the episode's plot, but considering how exciting the scene was and the less than thrilling send-off the villains actually got in a later episode; it's a shame it wasn't real after all.
Unintentionally Sympathetic: The Mutants of Plun-Darr - Slythe, Monkian, Jackalman, Vulture-Man - even though they're evil they're just so Blessed with Suck that sometimes you just can't help feeling sorry for them. This is not the case with their 2011 counterparts, however.