Putting up a new front door; old weather strip is accompanied by a hard black substance that looks like it may have once been soft but has long since hardened. I'm a little hesitant to chip it away as it looks a bit like a black mastic adhesive and the house was built in the mid 1950s . However, I've only know black mastic to be on flooring and there is no sign of it anywhere else in the house; any ideas as to what this stuff might be?
It sounds like you have it right. Older weather stripping like this is horrible. As soon as you chip it off I would do an assessment on what type of jamb you are dealing with, if it is kerfed - has a notch in it I would replace it with a push in type strip.
If not, use a weather strip with an adhesive backing, but never go back to that "goo" that is in there now.
Even though some of the wood is rotten I would still recommend replacing the strip as energy bills are high no matter where you are in the country!