whats the worst that could have happened

I feel like they would have been as hostile as they were under Onestar. Mudclaw probably would have still helped in the badger attack, and the battle in eclipse would more or less be the same...

Honestly, I've been thinking for a while, and he couldn't have been much worse than Onestar. After all, Onestar was trying to mimic what Mudclaw would have done in order to please his clanmates and be the leader they wanted. If you want to see what Mudclaw would have been like- just look at Onestar.

Though I suppose Onestar would still be considered a "Mudclaw Light", as I don't think he would have ever sent Crowfeather and Breezepaw to the mountains, nor would he have had a casual conversation with Jayfeather that one time, and let's be real, Onestar was all talk and no claws. Even during the 4-clan war he spat out his rant and then was never seen in the fight again. Mudclaw would have been a lot more involved in whatever his clan did.

Yeah that's true, Onestar was guessing just as much as we are. For all we know he could have assumed wrong. He didn't exactly ever have the best relationship with Mudclaw.

He'd probably be like Onestar for a while at first, but he'd also probably eventually calm down.

Definitely true. Nowadays, whenever I see Makuu from The Lion Guard, I think of Mudclaw and think of their similarities if Mudclaw had become WindClan's leader: arrogant and pushing their weight around, then being more reasonable though still jerky occasionally.

He would have been a lot like Blackstar. Not unnecessarily aggressive, but also not taking crap from anyone. The only reason Tallstar didn't want him to become leader was because he knew that Mudclaw wasn't going to roll over and show his belly whenever it pleased Firestar.

Mudclaw has never given any indication that he would threaten the other Clans. Every single time we saw him acting aggressively prior to Starlight was in response to some kind of threat. In RS, he was simply chasing off intruders when Fireheart and co trespassed on WindClan territory. Later on in the same book, his refusal to allow Bluestar and Fireheart pass was understandable. He, along with the rest of WindClan, was still upset that ThunderClan had secretly housed Brokenstar. Any other cat would have reacted the same way. Doesn't make it right, but it is understandable.

Now for his actions in Starlight. He had every right to do what he did. The deputy succeeds the leader; that is what the warrior code states. He had served loyally under Tallstar for many moons. He respected his leader and his decisions. He basically led WindClan during the journey. He earned his nine lives. And then to suddenly have that snatched away from him, who wouldn't react the same way? Mudclaw never had any ill intentions at all. We only see him through the heavily biased eyes of the ThunderClan cats. Step back and judge him just by his character, and anyone can see that he is nothing more than a dedicated, loyal warrior completely devoted to serving his Clan.

Mudstar would have been nothing like Onestar for one simple reason: he had nothing to prove.

Attempted uniting of the Clans under Mudstar's rule?

I'm not sure that comparison can be made between the two. Mudclaw was always present for WindClan, while Graystripe was gone for moons. Graystripe did lead ThunderClan in Firestar's absence during Firestar's Quest, but by the time he returned in the new territory, Brambleclaw had been serving as ThunderClan's deputy for a year or two (what's the timeline on that, anyway?) already. It's similar to how Mistystar was declared "dead" during Dawn...which, by the way, Hawkfrost still should've been deputy, because by those merits, Graystripe should've been reinstated like Mistystar was. Anyway, Graystripe was thought to be dead at the time, which made Bramblestar's deputy ceremony legitimate, while Mudclaw never went anywhere. He was very much an active, serving deputy while Tallstar was ill. Meanwhile, Onestar's deputy ceremony technically should not have been recognized, because the proper words weren't spoken, and that'd still make Mudclaw the "rightful" leader. That obviously doesn't matter, however, because StarClan still granted Onestar nine lives, so they clearly welcomed him as WindClan's leader anyway.

Your mention of the rebellion with the other Clans' help, though, is valid. It's not explicitly stated in the warrior code, but that's treason nonetheless, which is heavily frowned upon and illegal in their world.

I compared the Graystripes situation because we get direct confirmation from Starclan that either choice is valid (we never get this for Mudclaws situation but let’s just assume it did, unless you want to say they didn’t favor him and he was still valid somehow). Mudclaw feeling slighted is perfectly natural, deciding to perform a coup is another entirely. Especially when he hypocritically ends up indebting Windclan to Hawkfrost and agreeing to help him take power too(and who knows what ShadowClan wanted in return).

Mudclaw loses moral high ground when he started promising favors to obviously treacherous cats like Hawkfrost. Given his willingness to do that, at best he’s a useful idiot for Hawkfrost and at worst, one with just as little morality. Even with the generous interpretation, he doesn’t smell of roses.

If Mudclaw was really so popular, why not just tell it to Onestar straight up? Why not just pull a Needletail and say “Real Windclan goes this way”? This was all about him, not what Windclan as a whole needed or wanted.

As much as I like Firestar, I gotta agree.

Ah, yeah! I didn't mean to say that Mudclaw thought he was unseating a future bad leader, because he certainly wasn't. Well, he may have, but it would've been an assumption thing, since yeah, Onestar hadn't done anything yet by then. No, I mentioned what Onestar did further into leadership, because you said Mudclaw leading the rebellion as one of the reasons why he was in the wrong. Onestar did the exact same thing, if not worse, later on, so moral ground for either of them doesn't exist, and if it does, it's even. We don't know what Mudclaw promised Hawkfrost, and we don't know what Onestar said to persuade RiverClan (who are on the whole other side of the lake, so I don't even know what Leopardstar gets out of that, besides thinking she's knocking Firestar and his Clan down a peg or two. There's no mention if Onestar gave RiverClan a stretch of territory or anything, so I don't get why she was involved). Though like you also said, we don't know what Mudclaw would've done later if he had become leader. At present, however, we know the worst thing he did was lead a rebellion against a leader who was not rightfully chosen. The circumstances were definitely suspect, too, since like he said in the books, everyone knew Onestar and Firestar was close, while Brambleclaw was Firestar's Clanmate. It's the perfect setup. 

I do wonder how he would've reacted to the battles later, like with the Dark Forest. It makes me curious if he would've probably punished Breezepelt and the other traitors. I imagine he'd see it more as an embarrassment as Onestar, who defended them and declared none of his cats were traitors (which was hilarious in hindsight). I imagine Mudclaw might have defended them at first, and then been furious and let it known they were punished somehow. Him during AVOS would be interesting, since I can't see him having sired a kit by a kittypet. Then again, we never thought Onestar would, either sooooo... lol