Between the events of TDK and TDKR, Nolanverse Batman is forced out of his weepy self-enforced exile when he begins to hear murmurings about the grotesque mutilations/murders perpetrated by a new rogue known as The Jigsaw Killer. Can Baleman's skills bring John Kramer/Amanda/Hoffman/whoever the hell else was involved to justice before more victims are enraptured in Jigsaw's nefarious plot and Bruce can go back to practicing his indoor archery?
Yeah, of course he's going to CATCH Jigsaw, but how many victims will he save? I barely paid attention to the Saw movies, but I was under the impression that all of the movies take place in a relatively brief amount of time.
Eh, he couldn't find the joker without Joker wanting to be found or using the sonar tech he destroyed at the end of the film. Joker wasn't even hiding either. He was pretty bombastic about everything. Jigsaw should be harder to find.
Bats couldn't find Bane either without Catwomans help, and that was a trap that Bane made for him to walk into (which he obliged, and got wrecked).
Ras' found him, instead of the other way around (though I imagine it wasn't hard for him to deduce that Batman was his old trainee).
Batman from TDK series wasn't that great of a detective. The "He's Batman" argument doesn't work with Baleman, unfortunately. Bats doesn't find him near in time to save the victims.