I think a good part of it was the speed. He could just stand there and run the elements and geographical information through his head instead of going to twenty different databases to sort them out, and that was what got them to the children in time; an hour later would probably have been too late for the boy. But yeah, I was headdesking because what is he doing handling the forensics? Idk how it works in Great Britain, but there is a thing we have here called chain of evidence and with how the show presented the situation Lestrade's superior was unfortunately right to take exception to it.

(I don't think Lestrade WOULD have allowed Holmes to break the chain of evidence, as that's exactly the kind of thing the defense loves to pick apart and he'd know that; the best evidence is useless if it can't be presented in court. But that's TV for you; I headdesked at Murphy in Dresden Files going through a crime scene without gloves too.)