The way the NES and SNES work is that once per frame you read from the memory address mapped to the shift register to get all the bits out, one at a time. For certain inputs you only care if it's pressed now. Others you compare to previous state to see if it changed.

Bounce could, theoretically, cause an input to be read as a non-input if it just bounced at exactly the wrong time, but it won't cause multiple inputs, as it's only polled every 1/60th of a second.