Here is a mystery unsolved which was bugging me for decades - it’s about the iconic white railway clocks that used to be on all railway stations at least in Germany. The thing with these clocks is, that once every minute, the hand for the seconds stops for a period of time which is noticeable longer than one second, and I always wondered why this is the case. My most favorite explanation (they do that so that they can fake that their trains are on time) doesn’t hold after even the slightest of thinking it through.
Addendum: Related: A Wobbly Clock