An unspecified number of things you may or may not know about Desmond
1. He's weird. He was weird before the island (what normal person follows up quitting medical school by planning a race around the world?), he got weirder in the hatch (three years with little to no social interaction, especially after Kelvin died) and he's been getting weirder since he left (the timing of which is purposely being left vague for now).
And by weird, I mean ... he's not really crazy. Not really. He's just got a very odd outlook on life, and he thinks it's perfectly sane.
2. Sort of tied in with the above: he knows things. He won't tell me how he knows them -- whether he's been in contact with Dharma, whether he's spying on the survivors (before or after they found the hatch), whatever -- but somehow, he does. He knows enough to reference the polar bear, Danielle, the Others, and so on. (Though to be fair, I think Jack mentioned the Others in canon, and certainly in the bar.)
Also? He may or may not know about the symbols on the countdown, and about the map. I don't think he knows about the question mark hatch, though.
3. He's read a lot of books. A lot. This is mostly from three years in the hatch -- it's fair to say that any book you see there on the show? He's read. (Millicanon-wise, there's also a few Discworld novels there, along with 'The History of Tom Jones, A Foundling', and for great meta, 'Robinson Crusoe'.)
4. He's rather fond of Dharma Initiative products, food and otherwise. This is probably just force of habit, but it's also what Bar provides him with if he doesn't specify something (like Guinness).
5. Speaking of which ... obviously, he has no currency of any kind. His tab is just going to keep growing until he finds some. But, occasionally? He'll put a drink on Jack's tab. He feels the doctor owes him, after all.
6. He likes the Stargate movie, but he watched the first series of SG-1 and got a bit annoyed with it. As for other things, he's quite fond of the original Star Wars trilogy (he's seen The Phantom Menace, once, and can go either way in his opinion of it), and he also really likes Star Trek: The Next Generation. The other ones are okay, but TNG's definitely his favourite.
7. He doesn't like cookies. (I feel it's important to have at least one such pup.)
8. He is almost fluent in French. Not quite, but almost. He's actually kept this up, because there's books in quite a few languages in the hatch, and he's also fond of randomly switching to French when writing anything. He also knows enough German to get by without looking like a stupid tourist -- just a mediocre one.
I'll probably add to this in two weeks time. Or, alternatively, stare in dismay and then go off to a corner and cry.