Some first year models were affected with porous cylinder head castings, but no issues on the '04. Also there were some production runs that had slightly soft surface treatment on the cam lobes, leading to spalling, but no one has ever had any sort of failure related to that. Some say it just gives the oil more places to hang on the lobes.
The paint job could be indicative of crash damage, but the bike in the pic has exposed frame siderails and this is where severe crash damage would manifest with a punched-in area where someone has placed frame sliders. If you buy it, remove those and get some proper crash bobbins which mount to the front of the motor, not to the most vulnerable part of the frame.
There are no 3rd thrown rod issues with the ZZR 12 motor. Although the architecture is the same as the 11, it's a more robust unit. Run the occasional jar of Techroline in the fuel tank and you won't have any carb issues. Most common carb problems come from amateur tech fiddling leading to torn vacuum diaphragms, missconnected vacuum lines and stuck floats. Many owners install the "poor man's jet kit" which is one or two .020" washers under the needle clips, raising the needles slightly. At some point, the rubber o-rings that isolate the main jet may fail, but the fix is easy and cheap. In places where there's no ethanol in the fuel this is less of an issue.
It may be a pig, but it's a pig with a rocket in it's ass!