Prepare for a long rant...
Law enforcement in Pokemon is ineffective at best and nonexistent at worst. Even Looker just has your character do the hard work of tracking down culprits like Charon and the sages, then swoops in when the time is right to easily take them into custody. Of course it's all a plot point to make your character the hero... if Pokemon was at all based in reality, Team Rocket would be using assault rifles and machine guns instead of Rattatas and Zubats. And they'd be much more successful, too. I wouldn't imagine some 10-13 year old would last long against a hail of bullets from an AK-47.
But for a series where you basically take the law into your own hands, Pokemon does very little with the idea... you just battle the heck out of the bad guys and that's it. Why not have your character actively investigate them? Wiretaps, collecting DNA, comparing fingerprints and footprints found at a crime scene... surely these would be much more engaging "minigames" than dressing up your Pokemon or making them play sports. And they'd actually tie in with the plot. Pokemon essentially makes your character judge, jury, and executioner instead of actual law enforcement, but fails to run with the idea.
And as for the Pokemon League? I get the idea that they're too content sitting in their comfy chambers to get up off their fat behinds and do anything about the crime that plagues their region (with Lorelei (FR/LG) and Lance (G/S/C) being "kinda" exceptions... they at least get up and get out to investigate, but leave most of the hard work to you). It's like they have tunnel vision...they're only focused on the next challenger who comes walking through their doors. The Gym Leaders in B/W were somewhat better about this, but still...
As someone who is very interested in how law enforcement investigations in real life happen, I am disappointed by the lack of effective law enforcement in Pokemon games. Especially since dealing with organized crime is a key plot point in the games. Even if your character is supposed to stop them by their lonesome, at least have them do ballistics testing or witness interrogation - something that even remotely resembles a real law enforcement investigation.
But hey, we can start by actually arresting the kingpins of the evil crime organizations and making them face justice! Giovanni? Ran off, appeared at some tourney thing in Unova. Archie and Maxie? Ran off, who knows where they are now. Cyrus? Stuck in the Distortion World. Ghetsis? "Butterfingers" Alder and Cheren let him escape, allowing him to regroup, resurrect his gang, and strike again. Note that none of these include "serving life without parole in a correctional facility."
Oh yeah, and adding a few Ford Crown Victoria police cruisers into the game would be a great idea, too.