Got nothing against true crime, I consume loads of it, but it would otherwise dominate this discussion.
For me, the most compelling mystery is what was sweating sickness, it hit hugely in Tudor times and may have claimed the life of Arthur Prince of Wales.
The sheer speed of it rules out plague, as does the fact it tended to kill the young and fit and hit the affluent more than the poor. It vanished at the end of the 16th century and remains a mystery (some say ebola, some say anthrax contamination).