If an organism with multiple nuclei, such as the slime mold Physarum polycephalum, was to be exposed to a mutagen, such as 5-bromouracil, what would be the effect (besides death)? Especially if multiple nuclei were effected differently by the exposure.

I'm afraid there isn't one answer to that. Mutagenesis  is by nature a random process, so the exact outcome simply cannot be predicted. This is of course further complicated where there are two nuclei, so some mutations could happen in one and be rescued by the other.