Hmm, that's weird, it's now working just fine. All I did was exit out of the game, start it back up again and try out some of the other missions. I played through Hoth without a hitch. I fired up Tatooine (but got stuck in some background architecture near the beginning and had to quit, that was silly). The next time I started up I went to the Jedi Temple and it was fine (though the game did freeze up and crash when I got into a saber lock with a "training droid" later on in that level).
So I guess this just a glitchy game as everyone has been saying, but the "skies" problem has been solved. I already sent a support ticket to Aspyr media. I wonder what they'll say (if anything).