Weeeeeell the point of Lord of the Rings was that somebody was going to find the Ring sooner or later and it's lucky that the good guys got their hands on it.
Of course, Lord of the Rings wasn't written with the intent of selling Mumm-Ra with Sword of Plun-Darr action figures.
Anyhow, on TOS Plun-Darr was the name of the Mutants' home planet. So the sword was named after the planet. Here, the mountain would presumably have to be named after the sword.
(The whole Rataro/Ratilla/Jaga thing was a nice nod to TOS too.)
Anyhow, the biggest problem with Space Conqueror Mumm-Ra is that it pretty much abandons the whole "mummy" premise. Sure, he wears bandages and lives in a pyramid, but...the mummy archetype in monster fiction is all about explorers stumbling on ancient evil. It's interchangeable with the Balrog in the Mines of Moria, or pretty much any given Lovecraft story.
The first episode gave us just a taste of that, of Mumm-Ra being an ancient enemy who had awoken, but ever since the Mumm-Ra in Space episode, that's been completely absent.
The early episodes of TOS did a pretty good job with that -- the Thundercats only happened upon Third Earth by chance and accident; they disturbed Mumm-Ra's rest and threatened his rule. He's got a great Villain Monologue at the end of Pumm-Ra, when he's infiltrated the Cats' Lair and they're driving him out, where he says that they've got it backwards and it's they who have invaded HIS home.
Course, TOS kinda lost track of that idea after awhile too, to the point where in the last season he follows them home to Thundera to keep fucking with them, which kinda undercuts the whole idea of him just wanting them to leave him the fuck alone to rule Third Earth in peace.
Anyhow. They don't use him as much in TNS as in TOS, which at least to some extent makes him a scarier and more credible villain just by virtue of not having him stupidly defeated by his own reflection each and every day. The last time they beat him through Unexpected Resurrection, Distraction, and Go-Go-Gadget-Arms, and the time before that he didn't even show himself, he played the much cannier card of playing on Lion-O and Tygra's baser feelings toward each other.
And I imagine that, like TOS, TNS will have him much more evenly matched with Lion-O once he gets his hands on that sword.
A couple things bugging me about current continuity: first, they've pretty much just left the Stone from a few weeks ago dangling -- the episode where they were climbing the mountain to get it and were ambushed by the Mutants. If Lion-O misread the MacGuffin Radar and it was actually directing them to the Sword of Plun-Darr, then okay, but that hasn't actually been explained; near as I can tell there's still a Power Stone up on that mountain that they just kind of abandoned.
The lack of a home base makes the whole thing feel a little more aimless, too. I grant that it makes Third Earth seem a lot bigger than it did on TOS, that they can't just go home at the end of each episode, but the Tower of Omens could give the show some grounding, make it feel more like they're building something than just running around on a collection quest.
Then again, now that they've rescued some refugees (something that TOS didn't tackle until the last 20 episodes) maybe we'll get some more rebuilding going on. Lion-O told them they could resettle near Thundera, which could be kind of a big deal.
