They're pretty solid, despite what some Suzuki-loving half-kiwi, half pom weirdo might claim...
possible/likely problem areas are all typical 80s Kawi problem areas:
1. Frame cracks.
2. Slipping kick-starter.
3. Jammed/broken power valve.
4. Floppy footpegs and/or broken footpeg springs.
The forks will benefit from some Gold Valves if you are chasing performance. Like all older bikes, the stock springs (F&R) are far too soft.
My 88 KX250 benefited hugely from being jetted down, particularly on the pilot. Don't know if this is relevant for US fuel/altitudes, but worth looking into.
The 89 tank is a bit of a prized item, considering it is a one-year, one-model only part. The rest of the plastics are dead easy to get, considering they were the same as the 88~04 KX500.