The Mariner basically fails pretty hard to emote at all throughout most of the movie (blame Costner). On the other hand...maybe it has something to do with him being part fish. Think about it.
Much simpler explanation for the understated acting job: the character spends something like 95-99% of his time with only himself for company, with brief interactions with (likely equally undersocialized or possibly crazy) sailors or suspicious, backwards atoll-dwellers (who he seems well aware would kill him if they knew what he was) being his only interaction when he does communicate with others. He's probably lived that way his entire adult life, why exactly would he be an emotive and charismatic sort?
This troper just watched the movie for the first time in a few years and realised an extra dimension to the mariner flipping out at the beginning when his limes get stolen - he needs them for the vitamin C
If there's no one living on Dry Land, how could a map to there exist?
They do make a reference to longitude and latitude, but longitude is impossible to determine on a uniform, featureless sphere, so the point is still valid.
There were two dead bodies on the island. They could have tattooed the map on their daughter and sent her out to sea to bring others. Of course, there isn't much to go on in the movie for that theory but it makes sense.
The highest point of Dryland has a geological survey marker identifying it as Mount Everest. If they're sufficiently adept with Lost Technology to know how to use coordinates they're clever enough to know where Mount Everest is.
Here's another headscratcher: Assuming that these Atolls are all built using salvaged materials from the ocean floor, what's keeping it all afloat?
The shape? A rock, properly shaped, can float, despite it sinking, well, like a rock in normal circumstances.
Indeed, it's called a metal-hulled boat.
How did the beach erode away to sand in such a short amount of time geologically?
Well, to be fair, if the oceans rose that much, the atmosphere would rise with them. And Nepal's latitude is similar to Florida's, so it's not that far-fetched that it would be tropical.
Forget that, how are there horses on Mt. Everest but no sign of human habitation save a few mud-and-stick huts and some long-dead corpses?
How the heck could there have even been enough water in the first place to swamp almost the entire surface of the Earth? The idea that even Antarctic meltwater could cover, say, all of Colorado is preposterous.
As the Mariner and Helena escape, he shoots a harpoon at the gunship and tows it to blow up the Big Bad's boat. Except, there were two kids on that boat who were using semaphore flags. It's not shown, but only the Big Bad manages to (just barely) make it off, and he loses an eye in the process.
He also blows up the Big Bad's boat at the end for no particular reason, which is packed with dozens if not hundreds of men and women who simply want to find dry land, taking out what could well have been one of humanity's last hopes to establish a stable, genetically-diverse population.
Since we are already on the subject of genetics - it requires a population of about ten thousands to avoid problems with imbreeding. Another five to be extra sure. Not even Smokers had such numbers, so humanity is screwed anyway.