About every 15th start I get the sound you hear if you try and start the engine if it is already running... you know... the ugly starter screech. Do I need to rebuild the starter, or is it the flywheel missing some teeth, or something else entirely? It is a 67 SS350 with original starter and 85K miles.

Had a similar thing happen; there wasn't enough juice to keep the starter engaged and it would kick out. Since you're still holding the key in start position, it immediately attempts to re-engage. Nasty sound.

Turned out to be poor battery cable connectivity. I cleaned the ground cable, but the positive was questionable, so I replaced it. No more problems.