Fabric: Tough, not floppy, as waterproof as possible.
Ortleib style PVC and Carradice canvas are both good. Quality cordura is OK, cheaper stuff delaminates and frays after a few years.
Stiffening: Light plastic board in the back and base. Avoid heavy card, wood or metal stiffeners.
Shape: A heel cutout profile allows mounting further forward for better weight distribution.
Closure: Zippers are the first to fail. Rolltop and flaptop are reliable. Extendable collars permit overloading with bulky items.
Mounting: Quick-release, locking systems are the way to go, avoid hook and elastic and velcro.
Ortleib and Rixen&Kaul are the best systems; you need a solid, one-piece hook + a rotating lock widget. Some systems have a hook with a built-in hinge that is spring loaded. If the hinge fails, the hook fails and the bag falls off.

Locking hooks require a tube or rod of round profile. They do not work on twin, welded sections and at cross-bars. Look of a rack with plenty of free, single-section rod.