Check for:
Rear Wheel alignment ( physically measure, Don't go by the lines)
Hanging Brake Caliper
Verify if a Power Commander is in fact installed. If not the bike will be running lean from better exhaust flow. From the pic it looks like you have the full Yosh system and not just a slip on. If that's the case a power commander is highly recommended along with the Pair Valve block off plates.
Look to see if all the stainless tubing located between the exhaust header and the engine block is still there. If it is, this is more than likely your problem. Look up "Marble Mod" and see if that doesn't help with the backfiring. ( This is the Pair Valve Mod everybody is talking about)
Low pressure on tires will also create a "lazy" feel on handling.
Removal of the extensions will give you the stock cornering ability.
This is a Busa, Not a litre bike. While it will still hang in the corners with the best of them it is not 'Flickable" as it is too dang big!
Lowering the front and or rear will also have effects on the bikes turn in abilities.
That rear reflector that's blinding everybody in the pic is more than likely the culprit though. It's acting like a lopsided wing
Check for play in the swingarm. Perhaps it was monkeyed with by the previous owner.
There's really nothing you can do about the sound of the Yosh exhaust Besides replace it. I highly recommend the HMF Dual Hi Rise exhaust as a remedy.
Checking these few things out may help you discover your problem. Good Luck and ride safe.
