One would be the rear brakes locking up too easily when one brakes strongly. Another (if the limiter fails to let any fluid through) would be no braking at the rear of the car at all, which could have catastrophic consequences, as all the braking efficiency would be on the front wheels. A M.O.T. test would fail a car for the second suggestion, but not necessarily for the first one.
The handbrake's action would be unaffected though......