To push simplicity to the fullest, you don't even need the Arduino. These photodiodes produce current when illuminated.http://www.sparkfun.com/products/9541
You can put ten of these in series across an Led and it will light the led if and only if all 10 diodes get light.
You could also insert a 9v battery in series to brighten the "On" condition.
Your test sheet is placed on top of your rigged one, which has a photodiode at each hole.
When you illuminate it, the Led will go on only if all photodiodes get light. Any one in the dark keeps the light off.
You then would manually check which hole is missing. You do get a quick instant and reliable pass, though.
You could expand the Arduino solution to general purpose and have a dozen or more inputs.
You take a new good sheet and stick any of the magnetic mounted diodes on each hole.
You'd have a "Learn" button which, when pressed, learns which ones have to see light in order to pass.
You then have a big "Test" button that sounds the alarm if the new readings don't match the learned one!