Badquaker posted an excellent list.
wlg,
The round that "stayed in the barrel", was it a live round you didn't fire that was stuck in the chamber or was it a bullet that didn't leave the bore (lands and grooves) after being fired?
If it was stuck in the chamber, considering you were using factory ammo, you could have an improperly sized chamber. It's unlikely, but it does happen. A chamber that is slightly tight could cause all the trouble you're having.
I do not agree with putting 500 rounds through the gun if an obvious problem can be discovered early. It would just be wasting rounds. An unfired round being stuck in the chamber is not something that will likely fix itself by shooting a few rounds.