I've heard a lot about the older models with the 5.7 hemi having an issue where the valve seats would drop randomly and destroy the engine. I'm looking at buying a 5.7 L hemi but I'm worried about how common this issue is??

 

Seems to be fairly common, from what I have read and seen it's happening to cars with between 160,000 and 200,000km (whatever that is in Miles) after the engine has overheated.

My theory is that's when the thermostat has failed/stuck closed causing the overheating to happen.

If you are going to buy one, change the thermostat!