I saved this post a while ago for the next time someone asked this question...
Provided it's had reasonable care taken of it, they're good, reliable bikes.
Here's some stuff to check before you buy it...
Firstly, the FZ6 drops into first gear like the Crack of Doom! This is, incredibly, absolutely normal.
Check the exhaust headers for signs of rust. If they're bad, it means other, important work probably hasn't been done.
Put the bike on the centre stand and get someone to push down on the back. Using fingertip pressure, tip the handlebars to one side and the other and see if you can feel any grinding, clicking or rough sensations which could indicate the headset bearings are knackered (which is a bugger of a job to fix!)
Also take hold of the front wheel and see if you can pull the forks back and forth which would also indicate a dodgy headset.
Bounce the forks up and down and look for any signs of oil leaking from the fork seals.
Check the rear shock and see what condition it's in. Clean? Rusty? Can you change the preload setting or is it stuck in place because it's never been moved and it's covered in crud?
Put your finger under the chain a little bit back from the centre stand and try to push it up against the swing arm. If it goes really easily or you can't get it there at all, it's too loose or tight. If it takes a bit of effort to hold it there, the tension is probably ok.
Feel the gaps between the teeth on the rear sprocket, if you can feel a "lip" or a "hook" instead of a smooth curve, it's on the way out and would need replacing as well as the front sprocket and chain.
With the rear wheel off the ground, check to see if you can wiggle the wheel or swing arm back and forward or from side to side. Either could mean knackered bearings which would need to be replaced.
Run the bike until it's warm, then switch off and let it sit for a few minutes. Check the oil level on the centre stand and make sure it's ok.
Other things to ask...
If it's done nearly 24k (or 48k) miles, ask if the valve clearances have been checked, if they haven't and they need new shims, that's an expensive job if you get it done by a mechanic.
The brake pipes are supposed to be replaced every 4 years, so ask if they've been done (although did mine after 14 and they were fine, I just want braided lines).
Ask if the spark plugs and oil filter have been changed (recommended every 12k miles) air filter (25k miles)
None of these last ones are necessarily critical, the FZ6 is pretty reliable, but it would show that the bike has been cared for.
There's probably more, but that's a few to be going on with!
If you're happy with it, enjoy!
