1) The points of the tree must lie parallel (or within 10% of parallel) to the horse's back - not the shoulder, but the back. Points of the tree and angle of the back are highlighted in red:
#2) There must be even pressure under the tree points from top to bottom. In the photo above, there will be more pressure toward the bottom of the points; if the tree's too narrow, the pressure will be greater at the top of the points.
#4) There must be adequate clearance between the gullet and the withers. "Adequate" will vary from horse to horse - sometimes it will be 3 fingers, sometimes 1. "Adequate" just means that the saddle is sitting in correct balance and at no time makes contact with the withers.
#5) Balance of the saddle must be correct, with the deepest part of the seat being the lowest point. Here's a saddle with the balance point too far to the rear as a result of a too-narrow tree:
#6) The panels must make even contact with the horse's back, with no bridging or rocking.
Here's a saddle with correct balance:
#7) The tree of the saddle cannot extend past the 18th thoracic vertebrae, which is the location of the last rib and therefore the last part of the back capable of bearing weight.
So there you have the seven basic points. Next entry, I'll go into greater detail on each point.