What is the difference between a police motorcycle and a regular motorcycle?
Lights, siren, transceiver, and the shotgun (or MP5) strapped to the back. 
Mechanically? I don’t know. Police cars often have the most powerful engine available, and heavy-duty cooling. (Dad had the ‘police package’ on his Ford Galaxie 500 7-Litre.) Motorcycles already have good power-to-weigh ratios, so I don’t see a need for such provisions.
I have a retired police motorcycle - '02 Harley FLHTPI
Differences from the Harley Electra Glide platform, it was equipped with a very comfortable air-ride saddle (it had its own little compressor and air cushion), run-flat tires - mostly meaning an extra wide bead that wouldn’t allow the tire to fall off the rim if it was running low on air, a different wiring harness including hook-ups for auxiliary lights and siren, no existing wiring for stereo hook-up, an in-dash jack for a headset, handle bar controls for lights and siren, more chrome than a standard Electra Glide and a beefed-up alternator. Other than that, it was a standard issue Electra Glide.
It was used in-service for two years and sold to the civilian market through a Harley dealership with 3,000 miles on the odometer.
I’ve modified a number of parts since I bought it including a new two-up seat, touring trunk and a bunch of other stuff. But it still stands out as a police bike. Picture here.
Hey, my friend has an ex-police motorcycle (Kawasaki KZ-1000) and has most of the differences the guy above posted (seat, electricals for siren/lights etc.) The plastic fairings are also different but that’s pretty much it, it’s the same bike mechanically as a street kz-1000.
My recently-acquired '90 Crown Vic lacks the storied engine and suspension, and weighs several tons more, but that bastard can make its way faster than than any car I’ve driven over the past several years.
Except my MIL’s Roadmonster station wagon. Never rode with her at the wheel, but my wife never had a clue to how to handled that de-tuned Corvette engine. It’s awkward hoping that a relative might make a bequest, but I was there, an experienced construction estimator, laughing with my FIL at what his BIL paid for a barn that, all these years later, and after when the other residents, lacking Unc’s Bohunck frugality, sold out for a song.
I guess the most important part for a police motorcycle is a beefed-up alternator and rectifier. Most motorcycles have crappy electrical systems.
For example, my 2008 Honda Hornet’s alternator can do just 330 Watts. With all lights turned on (plus normal loads like battery charging, spark plugs, ECU) it is just barely able to cope with the load.
I can’t imagine putting a siren, extra lights and a radio. It will drain the battery in no time.
As most bikes don’t get aftermarket accessories to increase the load, being barely able to cope is the right choice by the manufacturer. Not being crappy; just being right.
It’s not . . . blue? 
CMC fnord!
(For those that don’t get that reference.)
Critical Mass, that’s a lovely bike!