The main issue with the 250F's is lack of normal maintenance. These little engines turn a lot of rpms and are a full on race configured engine that is not built for a long life, but rather a very high output of power vs size. This means they require regular maintenance and for the most part there are a lot of them on the market that just did not have that.
The biggest failure rate comes from broken valves. This is due to not replacing them when they start to grow and closing up the valve clearances. The valve breaks and then that in turn takes out the piston, head, rod, crank and the cases.
If you should elect to get one used, then if you have starting problems and find the valves need to be re-shimmed, then it's time to have the head reworked with new valves , springs, retainers, clips and have the valve seats cut or replaced as well as replacing the cam chain.
Also don't forget to replace the crank on as regular maintenance as well.
Paw Paw