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

If you have a good quality panel... Square D, Eaton, Siemens, etc.. you really have no reason to worry about a circuit breaker malfunctioning in such a way that it doesn't trip if your load is greater than its ampacity. I have never seen this happen to any manufacturers circuit breakers not named Zinsco. In short, circuit breakers work and they work well you dont have to be afraid of them failing. If you are really nervous, install a arc fault circuit interrupter breaker in the existing ones place... any arcing and it will trip. Or an arc fault/ GFI combo breaker that will protect you from every angle.
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.