The things Aaron told you are all good -- most of them without regard to whether there's algae or not.

But, I'd like to request that you do the 'fingernail smear test' to verify that you've got black algae: just scrape a bit of the algae so that it gets under your fingernail, and then smear the collected 'goo' on a white 3x5 card or other heavy white paper. If it's black algae, it will 'smear' dark green.

The distribution of the algae is odd, and atypical of any black algae I've seen, so I want to confirm that that's what's really there, before going too far down the drastic 'kill black algae' warpath.

One other request: when was your pool built?