I've had exact dream about this.
First off, the amount of missing people cases would sky-rocket, between Jynx and other human-like pokemon being mistaken for people, to things like Gotholita and Hypno kidnapping.
Secondly, religious loons would use them to either argue or prove their respective religions, not to mention the church would have a conniption and probably execute the poor kid who DARED fight Arceus/The Legendary Gerbils/Groudon and Kryogre/etc.
Thirdly, wars. Lots and lots of wars. Nuclear capability will be a thing of the past when any psychic, ghost, or dark type can just disable EVERYTHING, and instead of Nuclear Capability it'll be Poke-pability.
Fourth, Scientific community in SHAMBLES. The laws and theories of physics, electricity, chemistry, evolution, EVERYTHING being questioned. Not to mention how the findings of Steven Hawking, Einstein, Thomas Edison, and many more will be ignored for the endless knowledge of psychic types (Kadabra ALONE could probably wipe the floor with Deep Blue in a chess match)
Fifthly, animals would, more than likely, become extinct for the more superior Pokemon. Sure, some may slowly evolve (Darwin's version, not Oak's) into types of Pokemon, but in the long run, they will cease to exist.
And finally, The Olympics will be done with Pokemon.