Checking out the stirrup bars is essential. If you're going to use them properly, they should move easily up and down. They should also be secure. Any motion in the stirrup bars shows that the steel or wood is getting sloppy, or there are popped or sheared rivets. General appearance can tell you a lot.
Similar checks are necessary when buying a Western saddle.
Safety comes first, and a sound tree is essential. Push on the cantle. If you see movement in the middle of bars, the tree may be broken or there's something loose. Look for bare spots in the fleece lining underneath. Look at the stitching everywhere to make sure it's not rotting.