Not sure how realistic this is code-wise, but I was thinking:
Could there be a way to remove threads from view when clicking on "Show new replies to your posts"? I've often dropped a comment or a few comments in a thread and don't have an interest in re-visiting the thread, and end up with loads of threads I'll never read cluttering up the Unread Replies list. If there were a way to remove them from that page - e.g., with a little button labelled "stop giving me updates on this thead" or something next to each thread in the Unread Replies list - I think this would save a lot of energy for people, and possibly also for the server.
Just my two cents.
EDIT: Alternatively, there could be a little checkbox next to each thread on the Unread Replies list, with a button at the top or bottom of the page labelled "Remove".