In a nutshell, to make it easy for you:
1. Over-polished case leads to rounded edges and soft angles, and in severe cases, alters the geometry and shape of the watch case. An AP ROO case is supposed to be sharply angular and well-defined.
2. An unpolished case does not mean anything, the case can be full of scratches, dings, dents, marks, gouges etc and unpolished at the same time. Describing the case simply as "unpolished" tells only half the story. Check for case condition.
3. Turn the hands until the date changes. It should change instantaneously with a soft audible click as opposed to the datewheel rolling a little (you being able to see 2 dates or only part of the current date) before flipping.
4. Check the serial number and model number against the warranty papers. This is an older model so it should be on the first page of the warranty booklet as opposed to being on a card like the modern APs.
5. Just don't buy it if you do not feel comfortable about anything!