Question: Suppose I want to reduce risk of a circuit breaker malfunctioning and failing to disconnect a shorted circuit.

What if I install two identical breakers sequentially (one after another) so that if one of them fails the other one steps in and disconnects the circuit? Is there any problem with such installation?

Answer: 
Two breakers in series would reduce the risk of one failing in a way that stays in a closed (conducting) position. But modern breakers today have an extreme low risk of this happening. If I were that paranoid, I'd put a breaker and a fuse in series. But I'm not.
Logically, this makes some sense.

Practically, there is no breaker panel configured to let you do this. You cannot modify the panel, physically, without invalidating the U/L certification. 

Actually the [system availability goes down for mechanisms in series](http://www.eventhelix.com/RealtimeMantra/FaultHandling/system_reliability_availability.htm#Availability%20in%20Series), because you multiply the individual available availabilities.