I saw this called "one of the worst TOS episodes", so I watched it. Unfortunately it's bad in a boring way.
In fairness, the episode did two praiseworthy things that didn't work out. The lesser was to have a Barrymore (John Drew, father of Drew) as the main guest star. Unfortunately he didn't turn up for shooting. (In later life, he became a recluse and a derelict, losing his grip on his physical and mental health and becoming estranged from his family and children.)
His (substandard) replacement on this Star Trek episode was Robert Brown. This should have been a wonderful role, with lots of juicy madness and paranonia, yet Brown makes it dull.
The other and much bigger praiseworthy thing, though, apparently involved Lieutenant Masters, who was going to be a love interest for Lazarus (Barrymore/Brown). This is a parallel universe story, so that would have involved a love story between Masters and the sane Lazarus, letting the crazy one betray and manipulate her to steal the Enterprise's dilithium crystals. Sounds fun, right? Unfortunately this subplot was deemed unacceptable by southern broadcast channels, so it got replaced by pointless scenes exploring an uninhabited planet.
You see, they'd cast a black actress as Masters. Interracial romance on TV in America in the 1960s? Civilisation would have ended!
I'd have loved to see that version. It could have been entertaining and important, neither of which the broadcast episode achieves. Lazarus himself is boring, unconvincing and unclear. Brown isn't achieving anything worth a damn with the role, while I still don't know what was going on with what I presume is the swapping between them. That magical head scar, for instance. It's there, then it's gone, then it's back again. Why? Even in hindsight, I can't tell when we're meant to be looking at sane Lazarus or crazy Lazarus, or what difference it makes to the story. I'm not even convinced that sane Lazarus was necessarily ever in our universe at all, despite the fact that this would have been part of the Masters love story.
The frustrating thing is that losing the love story left the episode scrabbling about for ways of filling its screen time, yet they never thought to sort out the explanations or tidy up the plot holes. If that's sometimes sane Lazarus, then why didn't he immediately tell Kirk everything? Why does everyone think there's going to be an invasion at the beginning? (An invasion of where? The entire universe? As it happens that's not unimaginable since this is an alternate universe episode, but Kirk hadn't known that at that point.) What does it mean when Spock says the effect "was strongest here on the planet beneath us"? The universe briefly winked out of existence. Is there some kind of super-non-existence that's stronger than ordinary non-existence? Why doesn't Kirk put a guard on the paranoid lying saboteur lunatic, thus letting him steal the dilithium crystals? Why would an anti-matter ship be able to use ordinary-matter dilithium crystals? Why does that beard look so stupid? (It's inconsistent in its stupidity, but this might be a subtle production hint that we're looking at different Lazaruses.)
Then there's the science. Is anti-matter some kind of moron magnet when it comes to SF writers? What we have here rivals one of Doctor Who's notorious idiocies in this department (Planet of Evil). You see, sane Lazarus is from an anti-matter universe and so all existence will be destroyed if he comes in contact with crazy Lazarus. (As presumably happened at the start of the episode, except that, um, the universe was only destroyed briefly? Apparently this is due to the "alternative warp", a "negative magnetic corridor where the two parallel universes meet". If anyone can explain how this works, send your answers on a postcard.)
You might have noticed the interesting bit. The two Lazaruses have to meet to cause a matter/anti-matter reaction. Our Kirk can safely wander around an anti-matter universe. Presumably in Star Trek physics, a hydrogen anti-matter atom isn't just a hydrogen anti-matter atom, but one that knows, for instance, that it's from Lazarus's left buttock. Oh, and destroying Lazarus's ship in one universe will also destroy it in the other. "If I destroy his ship, won't yours also be destroyed?" "It will." Eh? This is where I throw up my hands and say that this universe clearly runs on handwavium, with a side-order of "whatever the scriptwriter wants in this scene".
In fairness, Doctor Who did something similar to this in Mawdryn Undead, but with time travel instead of anti-matter. The Brigadier met himself and caused a temporal overload. That I'd have bought, but with anti-matter I'm boggling. (My best explanation is that this simply isn't anti-matter at all and that Spock's detailed explanation came from his arse.)
Then there's the finale. Apparently Kirk has to imprison the two Lazaruses together in the alternative warp, "trapped forever with a raging madman at your throat until time itself came to a stop. For eternity." Seems a bit extreme. Why not just kill the crazy one? It also seems a bit of a stretch that they'd be fighting forever, unless this is simply a property of the warp corridor itself. You'd think it likelier that they'd fight until one of them got killed, collapsed of exhaustion, got hungry and went to look for some dinner, etc. Fighting is hard work, you know. I'd say that's probably a half-hour "eternity".
To be honest, though, I don't care much about all that. They're just plot holes. No, the problem is that this is a dry-as-dust episode with no human drama (thanks to 1960s American mores and Brown's bad acting), so technobabble is all it has. It's an ideas episode, but it can't make sense of its own ideas.
Even Kirk's a bit rubbish, partly because of the writing and partly because Shatner's off his game. He's nearest his Shatneriffic best in Spock's big exposition scene, perhaps because it's a big scene with his sparring partner, Nimoy. However he seems a bit rough in the opening scene and he's downright bad in one confrontation with Lazarus. If I had to act across Brown, I'd be struggling too.
As for how Kirk's been written, he's an idiot. He refuses to believe McCoy's story because it's a little bit strange, when they've been sent to investigate a universe-threatening phenomenon that goes beyond "strange" into "inexplicable". He talks to Spock similarly. I wanted him to piss off.
There's just nothing of interest here. Kirk is annoying, his crew do nothing and the guest star is the equivalent of a deranged street preacher. If you met him, you'd give him 10p for a cup of tea. He's also acted badly enough for, say, the line "walking powder keg" to elicit eye-rolling. Meanwhile the plot has been gutted of drama and all that's left is fifty minutes of technobabble that's fighting against all efforts to understand it. That said, though, I don't hate this story. It's not aggressively bad. I'd take it over lots of post-TOS Trek. It's just dreary.
"Sometimes pain can drive a man harder than pleasure. I'm sure you know that, doctor."