Our client has provided us further information about this issue.
About 3-10 times a day, they get complaints that the checkout buttons don't work. 99% of these customers use IE10. We have the IE10 browsercaps fix in place, a problem we'd reproduced prior to the fix. But these issues are occurring after that implementation and so far we haven't been able to replicate the new issues.
Our client has discovered that if they instruct users to downgrade their IE10 to IE9 mode, then the checkout buttons work for most people. This is mystifying. First, our copies of IE10 work absolutely flawlessly. If this were a global IE10 issue, then we should be able to replicate the problem.
The only conclusion I can make so far is that some users have their browsers set to "compatibility mode." If that's the case, then it should be an easy fix to insert the X-UA-Compatible meta tag forcing a particular version of IE.