They should be stable. Usually resistors only "go bad" when they burn-up, which normally happens after a transistor or MOSFET burns-out and shorts-out fist, causing too much voltage across, and current through, the resistor. (Or of course, it could be a poor design with a resistor not rated for the power it dissipates.)
Carbon resistors might be a little more noisy in critical applications like microphone preamps or instrument amplifiers, but I'm not sure.