We live in a 1996 mobile home and there has been black gunk building up in the faucet screens and in the toilets (both tank and bowl). Also when we wash our clothes it initially smells like rotten eggs. We are on public water, and no one else has this problem. The pipes are pvc and obviously not that old. I heard it might be our hot water heater but why would that cause the black gunk in the toilets? Any help would be appreciated. Thanks

Forget the water heater if you have the same problem with cold water.
Can you shut the water off at the meter and disconnect the service where it enters the trailer? If so place a sock over the open pipe and turn the water back on. Is there black gunk in the sock or does it smell bad? No? This puits the problem in your units pioping.
It could be you have mold growing in your pipes. I wouldn't drink the water until the system has been flushed out with chorine or bleach.
Good luck, Tom