I am not quite sure what you mean by "quantum uncertainty" in this context. If you mean "Are there quantum mechanical effects that can cause a bit to spontaniosly flip from 0 to 1?" The answer is yes in principle (tunneling) but no for any real computer.
The reason is simply that compared to more mundane sources of noise (thermal noise, shot noise, noise coming from the enivironment etc) QM effects are completely negligeble and computers are designed with a rather large tolerance to noise.
Note, however, that tunelling IS a problem in modern processors in another context; it gives rise to leakage currents through the barriers in the transistors which in turn causes problems with heating.
somewhat OT:
Data corruption due to "random" hardware problems is very rarely a problem in a computer operating under normal conditions (nominal voltage bias). The main execption is in e.g. space applications where "radiation harding" is used. High energy radiation CAN actually cause data corruption (by literally flipping a bit) so in order to avoid this they simply make the circuits bigger; this is why even state-of-the art satellites use very slow computers; typical sizes can be of the order of a micron (whereas the processor in a typical desktop computer is fabricated using e.g. a 65 nm process).