Any once-living organic material can 'go bad'.
Fresh mushrooms eventually develop a slimy, clear exterior-coating and soft, black spots as they begin their process of decay. Where you may still be able to consume them (if they're in the first stages of decomp.), it's not suggested, because the flavor will inevitably have degraded as well. Moreover, it's not within my knowledge what consuming the mold of a decomposing mushroom will do to allergies and/or the digestive tract.
DRIED mushrooms, however, will keep for a very long time so long as they are not exposed to moisture in their dehydrated state. The addition of moisture is key to bringing about decay, and adding temperature changes, the process will only be exacerbated.