This usually means sulfur bacteria, which both produce the smell and leave the black film behind.

These bacteria turn sulfate into hydrogen sulfide as they live, so the smell and the slime come from the same colony rather than from two separate problems.

Look for black slime in the toilet tank and on the inside of the aerator, darkened silverware, and a smell that is worse after the water has sat.

Do not buy an aerator or a filter before the well is tested. Treating the gas while the colony is still there puts you back where you started in a few months.