I'm going to skip around a bit here to address what is without a doubt the biggest plot hole in the story. Kain sent out his lackey to find MacLeod - okay, fine. Not sure how the hell he's going to pull that off, considering they needed to stop and ask directions to find a powerful immortal sorceror, and the world is a big damn place, but let's be generous for the moment and say that the pull of the Gathering is applying to him. It explains why MacLeod will return to New York. This still ignores one big problem: how's he going to get there?
What we see in the film is ludicrous. MacLeod, using all the resources he has and experience with modern society makes it to New York roughly a few hours before a man with nothing but the clothes on his back and complete ignorance of the modern world? And it's not as if Japan is right next to New York anyway. How'd he get there not only this fast, but at all! And still dressed in the same clothes he's been wearing the past four hundred years, instead of changing into something clean. This entire setup doesn't make any sense, and it exists solely to provide a reason for MacLeod to get into a swordfight with somebody. Hey, great that we're not having more gunfights like the last film, but you can't just handwave this away. What's more, we're going to see Kain come to New York later himself, and that's not explained in this cut. It's in some ways an improvement, because originally, Kain just kind of teleported there using the power of illusion, which begs the obvious question: why didn't he just do that to get out of the cave? The frustrating part of this situation is that there's no reason for this problem. We could have eliminated all the looming plot questions with some very simple changes to some elements without really changing the story at all.
Here's how I would have done it. Nakano shows MacLeod some strange artifacts he's forge, small things, which he says that when the time is right can be used to bring them to the place of the Gathering. When the time comes to battle Kain, Nakano tells MacLeod to leave, just as it happens. Nakano takes one of the artifacts from elsewhere in his cave, and when he sees Kain has arrived, he deliberately causes the cave-ins that seal all the exits and bury the other two artifacts. His intent is simple: trap Kain in here so he can never claim the prize, and he'll use his artifact to escape himself. However, when he discovers MacLeod has foolishly stayed behind (again, as happened in the film) he uses it and his power of illusion to send MacLeod to the place of the Gathering, sacrificing himself instead. Kain still kills him and gets his power, but knows that he's now trapped. Meanwhile, MacLeod, just for fun, appears in Manhattan while Henry Hudson is going about surveying the place, with a bit of humor after the tragedy we just saw. It can end with MacLeod sailing off on Hudson's ship, but looking back at the island to know he would one day return.
As I said before, Kain and company would likely succumb to oxygen deprivation after a few days and pass out. Eventually, now out of the cave, they'd awaken on their slabs and Kain could slaughter some archaelogists, as is his idiom. Then, when it's complete, he could find the artifacts among other things discovered by the researchers during their careful examination, and he'd know what they were and how they worked. Dead Meat henchman could then comment on there being only two of them, at which Kain chops off his head, since he's now useless to him. Kain and the remaining henchman could then use them to come to New York, and his order of "find him, just find him" could be used and make more sense (why didn't Kain just go himself; did he have dinner plans or something?), since the two would be splitting up to search the city. It's not a perfect solution, but it would at least spackle over the major plot holes in the story without having to sacrifice any of the elements - you still get the murders and the henchman arriving to kill MacLeod.
Okay, back to what really happens. We wind up in a kind of Lawrence of Arabia thing going on, which turns out to be MacLeod with his adopted son. They stop as lightning crawls across the sky, because now Kain is free and... and I guess we need MacLeod to find out somehow. This could have worked better if it was something only MacLeod could see, since we know that immortals can sense each other, but the boy comments on it as well. Eh, why make sense when you can be dramatic?
MacLeod heads back to his clay village and leaves everything here in control of his friend, Jack, including his son, so he can head back to New York. We have some shots of MacLeod practicing with his sword before he leaves; I guess it'd be easier here than trying that stuff at the airport. Get used to this, by the way, as we get to see a lot of MacLeod swinging a sword around while music or narration takes place. Between Highlander II and III we get the right amount of sword practicing, but the problem is that it was all in one and none in the other, so there you go.
Back in Japan, our archeological friends are confused by the double homicide on their dig site. The police, of course, let them in - I guess Japanese police are too polite to stop anyone from poking around the crime scene. This trust proves well-placed when Alex opens a pocket knife and cuts some evidence from one of the bodies. Yeah, good luck getting a conviction now.
In the desert, MacLeod says a tearful goodbye to his adopted son, John, and then takes off in a Landrover, the scene the cutting to him walking down the street in New York at night. Literally walking down the street, not the sidewalk, because immortals don't really have to worry about getting hit by cars, I guess. However, when he heads up an alley he gets jumped by a bunch of toughies. When a knife is pulled he jumps the guy, but gets shot a few times by another gang member. This cuts to MacLeod being brought into the hospital. Um, didn't the Kurgan get right back up less than a minute later when taking a clip from an Uzi? Sure, he's bigger than MacLeod, but MacLeod should have all his strength now, yet he's unconscious when wheeled inside.
What follows is a typical "It happens in Hollywood but not in real life" bit. MacLeod gets up and demands to be released. When people try to physically restrain him, he resists, gets a sedative, and is sent to the psychiatric ward in restraints. Yeah, let me tell you, if only life were that easy. However, the truth is, just because you're a raving nut, doesn't mean you can just get committed on a doctor's whim. I've seen doctors who can only shrug their shoulders while watching someone who clearly was insane, who was threatening to do insane things, and say that unless arrested or pronounced by a psychiatrist, there's nothing they can do. Just wanting to be released and shoving a doctor isn't going to get you committed. But if you think I'm being too hard on the movie, well, just give it a minute and the teleporting bad guy shows up.
So MacLeod starts to come around and he senses the henchman immortal is nearby. He's a sitting duck, but a crazy guy nearby thinks he's Napolean, so MacLeod convinces him that he's actually one of his lieutenants on a mission to kill Wellington. It's admittedly a funny bit, where MacLeod is freed and "Napolean" puts on his paper hat to create a distraction for him to escape. It's a bit contrived (again, a mental ward is not something you can just slip in and out of) but what the hell, at least we can get to the action part. On the way, however, we have a nurse come out, spot the henchman, and drop her crap while she screams. "Shut up," he mumbles without missing a step, to which I agree. He's a guy in a bloody costume, lady; do you crap your pants every Halloween?
So Henchman and MacLeod are in the laundry area (and really, you didn't expect them to wind up anywhere else did you? not in a movie) and Henchman decides to vent his frustration at four hundred years of being trapped by slicing up sheets and lamps as he comes at MacLeod. However, while he's quite good at taking out linens, he has to do what henchmen do, so he does the aim for the torso thing rather than trying to take out MacLeod the only way it would actually work. MacLeod pulls the "already lost" move, gets the sword, and lops the henchman's head off. So it wasn't a sword fight so much as a sword swinging demonstration, but at least there wasn't guys in lame black armor shooting machine guns at our wig-sporting hero.
After the Quickening orgasm is done, we see a Detective along with the wise-cracking CSI dude on the scene. The Detective Stenn says this is the work of Russel Nash, and he soon confronts him in front of MacLeod's antique shop. It's a nice attempt to tie this back to the first film, but unfortunately it's a B-plot in this movie that really goes nowhere. It'll provide some exposition, but nothing of consequence is really involved with this part of the story. Sure, the police story in the first film didn't resolve either, but it existed to bring Brenda into MacLeod's world, not for its own sake, like it is here.
Kain, in the meantime, has shown up in New York and gets involved in a three card monte game. Again, it's a scene that doesn't make much sense. First, he doesn't put any money down and he still gets to play. Second, anyone who cheats at three card monte gets a serious ass kicking, and not by the guy who works the cards. Three card monte is a hustle, and it's a carefully handled hustle. Again, it could've worked if Kain pretended to put money down (using, oh, I don't know, maybe the power of illusion?) and then we got a chance to see him deal with some street giant. That actually would have been good - Like Katana in the last film, Kain hasn't done much to impress. He's beaten a village of weak peasants, an unsuspecting henchman, and an old man. Instead he somehow steals the glasses off the face of the three card monte guy, causing the two to run off. Yeah, I'm sure the mob won't mind.
Back in Japan, Alex looks over the sample she took and realizes it isn't a fake, that the outfit the dead guy was wearing was genuine. Her colleague shows up with a bit of tartan, making them curious. Also noteworthy are some cave scratchings that translate as "There can be only one." Anyway, all the backstory material settled, Alex is on the way back to New York with all this stuff. I'm not sure why all this stuff would go there instead of to a Japanese museum; you'd think that if someone discovered evidence Paul Bunyan was real the US wouldn't let it get carted off to Europe.