Could it just be that the strings are old? I've probably had the guitar for 6 or 8 months. I've heard everywhere from 2 weeks, to 3 months as a recommended string change interval.
BTW, the intonation on the Low E string was WAY off. The rest were just slightly off. I also raised the saddle on the G string, and there's no more buzzing.
Thanks again for all of the help. Without it, I would have probably ended up paying a Luthier.