(This information comes from a member on one of the boards I belong to.)
1. Before you put your saddle on your horse's back, check that the tree is in good shape. The way I do this is to put the saddle between my knees and, holding it on either side, close to the pommel at the very front of the saddle, squeeze the sides together firmly. There shouldn't be any movement. If there is, or if you hear a grinding, it indicates a weakness in the tree, or framework, of the saddle, that can seriously damage your horse's back if you continue to ride on it. No saddle with a broken tree should ever be used on a horse.
2. If the tree passes muster, continue your check by looking at the bars of the saddle, where your stirrups attach. Make sure the bar on each side is secure and that no rivets are working loose. Get physical with it, wiggle it and pull firmly on the stirrup leathers.
3. Next look under the flaps and check for weak stitching on the girth billets (those straps that your girth attaches to).This is probably one of the most important checks you can make as far as your own safety goes!