Something I noticed in the prelude though is that the town around the lake still doesn't know what to do with the camp property. It was a functioning camp at the end of Jason Lives, but had been turned into private vacation cabins by the time of New Blood. Now, in Jason Takes Manhattan, there's a Camp Crystal Lake sign back up when a couple of the high school seniors are out for a private cruise on a small yacht. The community also went through a whole name change in Jason Lives that didn't stick. None of this is a problem though. It makes total sense that a community with this much tragedy in its history would have a hard time knowing what to do with itself.
Another thing revealed in the first part of the movie is that Crystal Lake somehow connects with the Atlantic Ocean (assuming that the lake is in New Jersey as suggested in the first film). When I first saw the yacht, I thought that it must stayed moored on the lake somewhere. But after Jason kills the two kids, he steers the yacht to the dock where the cruise ship is leaving from. So there must be a river that connects the lake with the ocean.
What I don't really understand about all of this is how Jason knows to go to the cruise ship. Maybe there's something on board the yacht that tells him, but why would Jason leave his familiar woods just to kill a bunch of kids on a boat? I don't know, maybe that's a dumb question and the answer is just "to kill a bunch of kids." Maybe Jason's just finally gotten tired of the forest. He's the walking dead at this point, so his thoughts are not our thoughts. It's not really a problem.
An actual problem (though still not a big one, I don't think) is all the time jumps in the series. Each movie takes place around the time that it was released, so from one point of view it's only been about nine years since Mrs Voorhees killed Kevin Bacon and friends in revenge for Jason's supposed drowning. But we've also seen Tommy grow up between Final Chapter and New Beginning, meaning that about 10-15 years passed between those movies. And Tina grew up during the events of New Blood, which have to take place after Jason Lives, because Jason is already in the water when she's a young girl. So that's another 10-15 years of movie time right there. Which means that if the first movie takes place in 1980, the main events of New Blood should take place around 2008 or so, not 1989.
The reason this isn't a big deal for me is because I grew up with Marvel Comics' retconning its historical references all the time. Whether it's Tony Stark's originally creating the Iron Man armor during the Vietnam War or classic Spider-Man's joking about Johnny Carson, I'm used to overlooking references that date particular stories in a long-running series. So Jason Takes Manhattan can take place in 1989 and we just push the first movie back to the late 50s, even though the characters and technology all clearly exist in the late '70s or early '80s. Works for me.
What doesn't work as well is Manhattan's attempt to fool around with Jason's origin story by emphasizing the Kid in the Lake legend. It's fine for Rennie's childhood trauma to be centered on the story of Jason's drowning, because that's what everyone believed for years. Maybe that's the only part of the legend she'd heard. But there's this weird suggestion at the end of the movie that maybe Jason reverts to his boyhood self as a result of being covered in toxic waste? That's just weird.
Toxic waste was a mysterious, magical substance in the '80s, so a nostalgic part of me likes the idea of it's having this weird effect on Jason, but it really doesn't make any sense if we take it literally. Fortunately, the Friday the 13th movies have a long history of figurative endings, starting with Alice's hallucination at the end of the first one. After I complained about how Jason Lives ignored the ending of New Beginning, a buddy pointed out to me that Tommy's attempt to murder Pam may have just been a nightmare he was having. So it's very possible - and I'm going with it as fact - that Rennie simply imagines seeing young Jason at the end, when in fact he's been dissolved by toxic sludge and (one assumes) sent to hell.