You might find: worn spots on the paint. You want to find original paint, and there will likely be chips or scratches. There is also the contemporary technique of battering new paint to make it look old. So value the chips and use them to your advantage. Do you see other colors or just the primer? If you're serious, you'll use a black light to discover if any touch-ups or additions have been made. New paint should fluoresce differently than old.
Steer clear of: fresh paint. If there has been a small repair or replacement, new nails should not be painted over. That would be a big red flag. And speaking of red, it's a popular color these days. Sometimes it's added to a painted piece, or even a painting, to increase desirability.