What you are describing is slime mold it starts out white and fluffy and spreads like a spider web.Later it will form a grayish mat around the base of the grass.Slime mold loves a wet acidic envierment,you can zap the mold with baking soda.Baking soda is alkaline and will alter the ph of the flat which is bad for the grass.Mold has to start somewhere during the growing process have you noticed anything that seems to start the molding?Does it start from a decaying seed,does it start on a very humids day,does it start on the edge and work its way in or in the middle?You can take proactive steps to limit the conditions that lead to molding.Pitch all the seeds that float they are dead and will just decay and cause problems.Rinse your seed 2-4 times to remove as much contaminates as possible while stimulating the seeds to come out of dormancy.Plant fewer seeds if aireation is an issue or use a fan to circulate the air.Use a dehumidifier to control humidity if your growing inside this can make a big differance.Once I put my seeds on the growing medium I dont directly water theme for 3-6 days,over watering is easy to do and simple to correct.Back off on the water until you can grow mold free consistantly,then start adding water until mold starts to return then back off a little.Just click on the words Image Gallery which is highlited in blue and you will arrive there.Then click on photos and scan down to grassmans sprouts and whala easy smeezy.How hot is it and how is the humidity,are you growing outside?Good luck and blessings.