I've let some of my Bhuts and Lemon Drops get over ripe and used'em fresh or dehydraded'em, and it didn't seem to affect the flavor. In fact, they seem to dehydrate more quickly.
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As I understand it, when a pod goes "overripe", which usually means soft, the cell walls have weakened and ruptured due to the natural aging (ripening) processes. While that will allow fungii to take up residence, there is nothing wrong with the pod itself in this state.

Some people - like me - find the mushy texture to be off-putting, so overripe fruit is usually bypassed. But there's nothing wrong with it. (Avocados, OTOH, do get bitter, as do a few other fruits, but peppers is not one of them.)

Dennis