You get one item off the bat for loading the demo and another for completing it; with all of the prompts the demo gives you, though, it was a bit misleading as to how much you had to do to 'complete' it. I made a valiant effort at clearing some of the quests but the H.U.D was so incomprehensible and the combat system so repetitive that I gave up with about 20 minutes to go and took a nap. Apparently, that works too—but you have to go through about ten minutes of gameplay to get to the free-roam segment of the demo in the first place.
You do unlock something via the ME3 demo itself (it seems as if that 'something' is only unlocked once you actually pop the full version of the game in next month, though), but there's a demo for the game Kingdoms of Amalur: Reckoning that, if played prior to ME3's release, will unlock unique armour and a weapon for you. Similarly, I've heard that playing the ME3 demo unlocks something in KoA:R. I have absolutely no intention of finding out what, though, as that game is a PoS.
You only get early access to the multiplayer demo if you have Battlefield 3. For everyone else, it opens up on 17th February.
Oddly, even though the demo rocked my little cotton socks, I'm backing you on this one. It's such a small taster to be given when the game comes out in three weeks—it's like throwing a tiny scrap of food to a fanbase that has been starving for months when they know they're getting a proper meal in a little while and just have to hold out for it...
It might be good for reeling some last-minute converts into the franchise, but for everyone already loyal to the series...well, for me anyway, it just made me impatient to get access to the full thing.