There are plenty of lists of science fiction mysteries out there: io9, Tor.com, and Best Science Fiction Books have all done good work on the topic. But as far as I can tell, nobody has included my favorite science fiction mystery, Nancy Farmer's The Ear, the Eye, and the Arm, first published in 1994. I suppose it's a young adult novel -- all of Farmer's books are identified as YA -- but it could and should cross over to adult readers.
It takes place at the end of the 22nd century in Zimbabwe. The titular characters are three men with mutations that afford them special abilities. They've formed a cut-rate, off-beat detective agency, and they get hired to find three children, siblings who sort of ran away from home and sort of got kidnapped.
Not too long ago, Farmer published The Lord of Opium, a sequel to The House of the Scorpion, another science fiction tale about scrappy kids. I'm crossing my fingers she might be at work on another Ear, Eye, and Arm novel -- or really, anything at all. I'll follow her wherever she goes.