is there anywhere in the world where either the FAA IR or the JAA IR is not accepted
In ICAO terms, if the IR matches the aircraft reg, probably OK everywhere.
If it doesn't match, there is very little one can do with it. IFR in Class G in the UK is one option I know of (yes, really useful
)
The Greeks validate an FAA IR, noncommercial flying, in an SX (Greek reg) aircraft, provided the owner is a Greek I believe, and that is currently the best deal I know of. I think there is a time limit, too.