Well, it turns out the site is still getting tons of errors now that traffic has picked up a bit. We're still working on it. We think we have pinpointed the problem, but have yet to fix it.
Here's some exciting news... In the near future, MySQL will be able to support clustering. This means we can balance the database load over multiple servers, whereas before we could not. Our current database server is theoretically strong enough to handle the current load (once we fix the configuration issues), but it will become a bottleneck as the site grows. MySQL clustering will ensure that the site can keep growing to meet demand. Yay!