Sounds like green hair algae.
+1 on the snails, let the tank keep cycling and keep your nitrates and phosphates down, that will starve it to death. Also keep up the water changes with RO/DI saltwater solution, using tap water with a "conditioner" almost guarantees you're adding phosphates to the tank.
Like meowzer said, a goby does a GREAT job on this, but you need to let your tank age a while longer before you introduce.