Different Width Tires?
 

By mistake I ordered two 20x700's instead of the usual 23x700's. I don't want a 20x700 tire under my butt for too long.

So I am thinking of keeping them to use in the front (obviously one at a time :) ) and ordering the usual size for the rear. It seems sensible me. Is there anything wrong with this set up?

No that'll work just fine. You may actually end up with even tyre wear front & rear.

However, I just don't like cornering with 20mm tyres on the front though. Due to the high pressure you have to use to prevent pinched-flats and to get any kind of rolling-efficiency, they skip and bounce over bumps in the corners badly. Not good for doing downhills or crits with confidence.