Yeah, that sounds like red slime algae alright (otherwise known as cyanobacteria). Hate the stuff. Things that cause it? Well, there's a debate right there. Excess nutrients (of course, as with any algae problem), but also low flow areas, lighting, lighting spectrum, chemical additives.....the list can go on depending on the person posting.
I can say from experience, that for me at least, my problems came from overfeeding and low flow areas. Once I reduce my feedings and redirect the powerheads the problem won't come back. Now, to getting rid of it in the first place. Well, I've tried the physical removal. Use a gravel vac to suck up as much as possible from the sand and rocks. Use a clean sponge to get any off the bottom part of the glass. Cleaning the filter media constantly to keep nutrients down....blah, blah, blah. Oh, it worked all right, but it took over a month for this to go away. The next tank I set up, the cyano reared it's ugly head and I got lazy and used Red Slime remover. Worked like a charm, didn't hurt anything, not the biological filter, not the corals or flower anemone, and the red slime was gone in 2 days! I will never go back to the physical removal.
Now I've heard of people using a regular antibiotic in place of the RS remover, but then, I've heard of some problems doing this too, so I that's kinda iffy. You can check around at RC, do a search and see what you come up with.......
Good luck!