I just added a link "Search by Subject" to the PM inbox and sent pages.
You can use it to find PMs that only match specific subject lines. You can enter partial subject lines.
Also, if you are already viewing a list of PMs only from/to a specific user, then the subject search is only applied to that list. If a user is not specified, then it searches over all PMs.
So if you go to your inbox (or sent box) and search for a subject, then you'll see the list of PMs from/to all users with matching PM subjects.
But if you click on "all from" or "all to" PM link for any user and get a list of PMs between you and that user, then entering subject search would bring up PMs between you two that match the subject.
Please let me know if something isn't working as expected.