I'm running the Giant Map on an older machine, and not having any big problems. I've had one crash, but was able to reload. Sometimes when I quit the game, it freezes, and I have to restart my computer, but the games are preserved.
I've noticed that on some loads, the music is choppy, or it sounds like it can't decide what to play. This is what was occurring during the one crash I experienced. I am guessing its a loading issue, because usually the problem isn't there. So in the future, if I load and the music is off, I'm just going to reload. When the problem isn't there, the game is very smooth still, even with all the civs hitting their expansion phases.
Knock on wood.
edit: Think I should point out, too, that I just popped about 3 dig sites per city. I mean, 3 dig sites within my borders, on average, per city. Didn't import resources though, used the generator. So, again, I'm guessing that the generator paints additional resources to what is already there, and what is already there probably includes did sites, so I'm getting double-whammied on the dig sites.
Unless you need something tested late game on Alpha 3, this might be a good time for me to stop the game.