Hi, I recently purchased an UNO and shortly after one of the two electrolytic aluminum capacitors fell off the board.I figured it would be a simple fix but then one of the legs on the capacitor fell off and basically (to my knowledge) there is no way to fix it. Frustrated in not being able to play with my new board I decided to plug it in to my computer and run a couple of basic sketches to see if it still worked(probably not the best idea) but to my surprise it handled "Blink" and "Fade" just fine but my question is how important is it to have both capacitors and what problems could arise if i continue using this micro controller. I have a project planed for it and don't want to have to wait to go and buy another(but that is the plan). Thanks in advance for your information!
They are for supply decoupling. Without it the supply produces more noise, might oscillate and is more susceptible to interference. This problem is worse the more current you draw so you might well "get away with it" on a lightly loaded system.