A/C Duct work should be fully insulated and should not sweat on its exterior. If its sweating on its interior and the moisture is finding its way out then your A/C isn't pulling enough moisture from the air. A cleaned evaperator coil & condensating line can help to remove more of the moisture. Open windows, cracks, or anywhere air from outside can find its way in should be sealed and repaired.
I have seen copper piping leak very slow from minute pitting. I found it best simply to cut the pipe at the leak and solder a fitting between the two cut ends. I certainly would not leave it leaking.