The mystery of why some people were so utterly convinced of the innocence of Louise Woodward (despite the televising of her trial so all the evidence was transparent), and why the same pattern is apparently being repeated with Lucy Letby.
The equally baffling concept of why the (completely innocent) Lindy Chamberlain and Joanne Lees were hung, drawn and quartered in the press, and all-but accused of murder.
The location of Peter Falconio's body.
The mystery of precisely how and why the Defoe (Amityville) family were murdered. We know by whom, and that's about all.
Disappearances of Richey Edwards, Claudia Lawrence and Suzy Lamplugh. And any and every missing child.
Exactly what happened to Michelle Bettles and Natalie Pearman, thought to have been possible victims of Steve Wright.
Of how many women Wright really did kill.
The truth of what happened to Caylee Anthony. I was working on a summer project at the time and watched the trial in its entirety, excepting around the last 2 days of the defence.
On the basis of the prosecution's case I believe (unlike the majority of the US populace) the jury reached the correct verdict. The Judge rather unprofessionally implied on TV that the jury were too stupid to join the dots between various connecting pieces of evidence (a job the prosecution should have helped them with in their summing up, rather than focusing on the emotive stuff). But the whole picture of circumstantial evidence didn't seem to me to reach the very high bar of beyond reasonable doubt, especially in a capital murder case. I'd have found with the jury.
That's not to say I think Anthony was necessarily innocent, but nor was there sufficient compelling evidence to prove her guilt.
Was the (very twisted) Flowers in the Attic novel sequence biographical, or was it just a clever marketing ploy? Who was/is Virginia/VA Andrews, and why is more than one author apparently writing under that name?