Wow. Don't get me started. I will save myself the rant as I have done it several times in the past. In short......
06/07 possible frame crack. Very few, but still possible.
All years, including 09, possible bad coils.
All years, including 09, possible stator/ rotor issue.
06/07 possible valve stem issue.
06-10 poor fueling IMO. Last ecu update was in 2011. I have a 2012, and can honestly say fueling is as good as any bike I've ridden. This is up for debate, as others with 2012 we're not happy.
Sorry I kept this short but all info can be had in great detail if you search, "crack" "valve stem" "coil" " snatch" or "stator". With all the info you will find you can make in informed decision on what bike may be best or you. Good luck. Even with its faults, the Gen2 FZ1 is a great bike.