Similar to "report a thread", these functions would allow a user to vote privately to move, or close a thread. When a certain threshold of votes is met, then the thread is automatically moved, or closed.
I find that most users don't like to be the Wendy Whiner and "report this thread", but they seemingly don't mind to suggest that a thread be closed, moved, or perhaps split into a different topic.
The vote count for suggested moves or closes might be publicly viewable, or perhaps only by moderators. Moderators could then view the votes threads have and act on them appropriately prior to an automatic move or closure.