I agree with the above, do you test for phosphates? What are your nitrate and phosphate levels? Your town water may not be the best thing for your tank. Is there a way you can get a copy of exactly what's in your town water? That should be free. Also, some fish foods, including frozen ones, contain phosphates. What brand salt do you use?Cheato is a macro (good) algae that will help lower your phosphates and nitrAtes. You say your levels are good but what exactly are they (especially Phosphates and NitrAtes). How many powerheads do you have in your tank? More circulation can help. Definately get more clean up crew, my hermits are chomping through my little flourish very quickly. I don't recommend you getting another tang as in my opinion your tank is not big enough (I have a 60gal with one Tang and she's outgrown that). I'd also test your water that your using before you put in you tank just to see what your levels are.
You said when you clean it, it tends to pop back up again within a week or so. Do you clean it during your water changes? Is there a way you can make your water changes weekly instead?
I had this problem when I first set up my reef tank in the beginning of the year. It looked exactly like yours. I was using regular water and not RO. I was overfeeding (purposely though because it was cycling) and I was leaving on the lights far too long. How long are your lights on for? What kind are they? How new are the bulbs?
If you have Green Hair Algae in your tank, your phosphates should read well above .05 mg/L., which is considered by many to be the lowest level at which Green Hair Algae will grow.
The above was taken from:
http://saltaquarium.about.com/cs/algaecontrol/a/aa070403.htm
There's some really good info in that article which is why I saved it when I had my problem.
I wouldn't sell the tank on the account of this temporary issue. It can be fixed! Please keep us updated.
Oh and I agree with beefing up the clean-up crew, keeping a skimmer running 24/7, maybe adding some phosphate removing media (do you use carbon at all?) and not adding another Tang.
Edit- I just noticed the reflections in your pictures. Does your tank ever get direct sunlight?