This morning I was deducted 15 points in one go. Now 15 is not a multiple of 2, and in any case the rep level at the question itself seems unaffected. So is this some kind of swingeing great FINE, in which case I would like to hear the charges against me and file an appeal, or a BUG?
It is probably due to your answer on "Should I use 'which' or 'that'?" having been accepted by the asker, and then un-accepted. An Accepted answer gives 15 points.
It is almost certainly the result of a question being removed, (either by the author or by the moderators), in which case all the reputation gained by others for answers or acceptances on that question is also removed. Try looking at your Reputation tab, ordered either by post or by date; you will probably see "-15 post removed" at some point. There is, by design, no way of telling who removed the post; and though it is occasionally possible for reputation to be conserved after such a removal, this is rare and depends on the historical significance of the post, not on your feelings about losing 15 points.
You might also try being more careful about your complaints. Levelling wild accusations of malice and incompetence simply because you haven't troubled to read the relevant sections of the Help is unlikely to predispose potential voters in your favour.