The purpose of a bridge rectifier circuit is to convert a sinusoidal input into a purely positive input, this means the negative have of the sine wave is inverted. It is generally followed by a capacitor that will convert the voltage to "DC". If one of your diodes becomes short the output voltage will vary depending on which diode is broken. Your entire input signal can be forced to ground, or an entire sine wave will apear in the load.
Best case scenario, your load recieves no signal, worst case scenario you force an inverse voltage on your load which can be bad depending on what your driving.