The minor annoyances:

• Can't close a ticket as a duplicate of another. You can merge tickets together, but this isn't ideal in all situations.
• You can't take a reply to an existing ticket and make it a new ticket without cutting and pasting it manually. This comes up every once in a while when a customer replies to an old ticket with a new issue.
• Can be insanely slow at times, if you have a large number of replies on a ticket. I understand this is improved in newer versions (we're still on 3.2.x)

I suspect most of these could be solved if I spent some more time on it, but they're really not annoying us enough for it to be worthwhile.

Not knowing anything about OTRS, I suspect the dogfood issue could be a couple of reasons: 1) OTRS possibly being better suited to a trouble-ticket system than to a bug-reporting system 2) a large base of existing info in Bugzilla that can't be easily imported into OTRS.

As for our setup, we've got RT running on an internal machine. It's not entirely dedicated, as it runs a few other services, but it's beefy enough to handle the load. Mail for support@domain and a few other addresses is directed to that box from our main mailserver. All ticket correspondance takes place through RT, but in the rare occurance that something tracking-worthy arrives in our personal mailboxes, we can just bounce the message to support@ and RT does the right thing.