Is there a free service for checking for common DNS errors on your domain? I previously used dnsstuff.com for this, but they since moved to a paid model.
There are several. I recommend Zonecheck, which is also available as free software that you can install on your own machine. The greatest thing about Zonecheck is that you can edit the configuration to change the policy (changing severity of tests from warning to fatal or the opposite, not running some tests, etc).
DNScheck is nice, too, and the only tool able to check DNSSEC.
I wrote a paper listing and comparing many online tools.
Try this one:
You should definitely check out http://dnscog.com/report/serverfault.com
They give a nice detailed report and supply some recommendations too.