Another Felix

Finding all the Police Officers causes Corey's identity as a Team Meteor agent to be revealed to his daughter earlier on. The Gym battle with Corey will be more difficult as he will have the field advantage.

I don't know about Corey's gym battle being more difficult, since it's a matter of what your team is. The change is that the gym battle uses one field effect if you find all the officers, and another if you don't. Both are good for poison types, but have different details.

Also if you find all the officers, Corey tells you more about his background.