Why would you need a shim for a PIII? I think part of the reason why some people talk about getting them is because their primary purpose was to help stablize the HS/fan on the AMD T-bird's core. This is because the cores are apparently somewhat fragile, and the force to lock the HS/fan down on the mobo (and maintain that pressure evenly), tended to make it more difficult to keep the HS level while attempting to lock it in place... The shim would theoretically provide an additional surface over the entire CPU that was supposedly perfectly level with the core.
However with the PIIIs, this really shouldn't be an issue (they run cooler anyway) and don't require the same amount of HS contact force.
One of the potential problems is if you happen to get a shim that is machined just a few mms too thick and you end up with improper contact between the core and the HS. Having this happen with a T-bird would surely mean a fried CPU... It's maybe not as bad with a PIII but the danger is there...