For example, in Goblet of Fire, when Winky the house elf is found holding Harry's wand after the World Cup attacks, the Ministry of Magic at first wants to take this as proof that Winky conjured the Dark Mark. They even know it was conjured with Harry's wand by using the reverse spell. The only problem is that they're fairly sure Winky didn't even know how to perform the spell needed to conjure it, as only Death Eaters seem to know how.
So the Ministry officials all stand around wondering, 'what do we do now?' and meanwhile I'm thinking, why not just check Harry's Wand for finger prints? Had they done so, they'd have found prints matching
Barty Crouch Jr., a convicted Death Eater
This person's prints being found on Harry's wand would certainly have at least pointed the Ministry's investigation in the right direction.
So, do magical investigations ever use Muggle techniques like fingerprints and the like?