A failure at creating a stable planet from a nebula, sure.
Which was it's main purpose. And it failed at that. That's a pretty good follow-up. In fact, many people (like myself) didn't like the Genesis-device in TWOK, and was happy they explained it away in the following movie. Otherwise? It wouldhave been a massive universe-altering device that is simply forgotten - like time crystals (stupid!) or sun destroyers (stupid!)
But it created a very impressive and stable cave full of life,
Genetic engineering is nothing new in Star Trek. There are simpler means to "create new life" than using instable proto-matter. This isn't even "fan-theories", this is self-explanatory in the movie. The breakthrough was not creating life. It was creating liveable
planets.
resurrected a Vulcan who died of massive radiation poisoning,
Well, it did resurrect his
body. Basically re-creating his Vulcan shell. But it was nothing more than a regular clone. What resurrected Spock as a person was his Vulcan "Katra" that was re-integrated into the body. As a "resurrection device" it's not any more usefull than, say, cloning a dead body.
Compare that to, say, Khans "superblood" which is completely able to cure the dead, and you have a "universe-changing device" done right.
and remains a very effective Doomsday weapon which is what the Klingons wanted it for in the first place.
Yep. But again: In TOS the Enterprise itself was said to be capable of completely wiping out entire planets. The Genesis device is just bigger, but not necessary more 'useful' for the Federation (or the klingons). The goal was: Bomb a planet, and immediately have your own planet (vs. have a useless wasteland). Bombing a planet was never a problem.
(Note: There were some ret-cons in the TNG-era, especially on DS9, where a Genesis weapon would have been usefull. But that is not the fault of TWOK/SFS - which adressed that - but of the later episodes that were in conflict)
They were in this week's episode for the first time. How can it yet be a fault that they weren't followed up on?
The problem is: They were stupid. And Im going to make a prediction here: They won't come up again. They neither made sense themselves (there wasn't even an attempt to explain them in the episode), nor did it make any sense for the character to have them (did he had them already in the klingon prison? If so, why was he in prison? If not, how did he get them so fast?), nor did the episode explain how they work, and nobody made an effort to include them in the resolution (they just needed one timeline where the "trick" him). All of which could have easily been fixed with one or two lines of dialogue. But as it was, they are a universe-altering device, never to be followed up upon, that weren't really important to the story apart from a superficial "what-if" romance.
That being said: This was clearly a self-contained stand-alone episode like we have seen them a thousand times before. So I'm giving way more leeway here. And it was quite entertaining, so I'm not even mad (or Mudd). That doesn't mean the episode was flawless. In fact it had multiple problems, this being one of the major ones. You can like a thing, and still see it having some flaws.