Back in 2014 and 2015, there was one ...
See Winter Bash 2014 Secret Hats Sadly, the Time Lord hat didn't look like an actual Time Lord's hat, as your suggestion, but rather like a Time Lord mode of transport:
Time Lord was earned by editing five questions that were posted more than a year ago.
The particular trigger for this hat was criticised, as it ...
I think using a standard format for answers to this type of questions would be a good idea.
I propose using
Year: Title by A. Author / by D. Director / featuring A. Actor
Explanation what it is and why it fits.
I don't think a leader board is a good idea, though, since it's not a competition. It's up to the querant to decide what the best answer is.
What you're asking for is pretty much implemented by the new SE-wide feature of being able to "follow" posts as well as bookmark them:
The Follow Questions and Answers feature is now live across the Network
If you've clicked "follow" on a post, then you will get a little red inbox notification for every new interaction (comment, edit, etc....