What PC parts can produce bright flash, and smoke, with the PC still appearing to work fine afterwards?

A burning capacitor could be your culprit. Regardless, if you saw a flash, or fire and noticed any smoke, the fact you've not noticed any problems simply means you've not yet tried to use whatever is broken. There isn't anything inside your computer that will keep on working happily after burning up. You should open up the computer and see what's been damaged. If you don't address the problem while things are working, you may have a small problem turn into a bigger and more expensive problem.

Good luck!

Almost certainly a Capacitor.

This happened to a Dell server that was running under my bed (don't ask, but basically to reduce the noise in my room) and didn't have enough ventilation.

Usually the area of the cap burst has smoke residue around it and in my case there was a strong smell associated with the burst and a 'pop' sound.

Server however kept on going....

I would bet a bug or other pest crawled into your power supply and was at the wrong place at the wrong time.

Open it up, if you have scorch marks on your motherboard, back up your data and replace your motherboard.

Otherwise, I'd replace your power supply as a precaution.

EDIT: Back up your data anyways. Also, do not open the power supply to check. If you notice nothing burnt/scorched with your motherboard or any other component in the system, replace the power supply.