So I've got documented cases in Chrome, Safari, and also Firefox (finally happened to me, I'd gotten the "Are you sure you want to leave the page?" prompts but before now choosing "No" had always prevented the double post). Tapatalk, OTOH, has had zero issues for me, which seems to indicate it is just slowness on the client-side somehow. I'm going to try and reach out to our hosting to see if they've made any changes to our dedicated server or see anything abnormal with load/etc, but they're usually pretty slow to respond.
If anyone has experienced a double post using Tapatalk lemme know, because that would blow open that theory.
I ran some VBulletin maintenance scripts last night and again today just before noon, but if it is still happening those didn't seem to do much.