What Predictions (Supposedly) Came True?
Uh... It's a calendar. It accurately predicts the rise of the sun every day. Otherwise nothing.
Why it Might be Bullshit:
First of all, the end of the Long Count holds no more significance than Dick Clark's Rockin' New Year's Eve: the Maya just had a celebration and then started a new calendar. Even they didn't think it was going to be the end of the world, and even if they had, why the fuck would they be expected to know?
As for the winter solstice thing, that's just when the Sun is at its greatest distance from Earth. Our poles shifting because the Sun is aligned with the center of the Milky Way makes about as much scientific sense as saying you shouldn't drive at sunset because your car might crash into the sun.
Besides, the solstice occurs in June in the southern hemisphere, so if the world looks like it's going to end we can all just move to Australia.