You've just come face to face with thehumidity balancing act we have to maintain(it does get easy though).
The spiderweb looking stuff is mold growing in the moss. Basically the moss conditions got wet, dark, and warm enough for the mold to flourish.
First thing to do is remove it, throw the moss away, and clean the area the moss was in to remove/kill spores.
Next there are multiple ways to prevent new mold from growing. What I generally use is just keeping the moss damp but not wet enough to start moss growing. The downside of this is that until yoou get a good idea of what level to keep the moisture at you will have to check it every day or so. Some people also sterilize(by baking or microwaving mostly I believe) the substrate before introducing it so there are fewer spores to start growing. You'll still want to keep the correct moisture with this method but you will have a larger safety range.
Either way resetup the hide with the new clean moist substrate and you'll be good for awhile. Just monitor how moist your keeping the moss and watch for growth so you can replace it immediately and get a better idea of the correct maintenance level.
As far as substrate what I use is sphagnum moss. If your herp store does not have it then you should be able to(for a much much cheeper price) get small bales of it from your local plant nursery. I get mine from a nursery, it's sold as green moss. The risk/drawback of this is the off chance of the moss having been treated or otherwise exposed to toxins. Because of this I would recommend ensuring it wasn't or smelling it to makse sure it smells natural.
Hope this rambling was helpful.
Sean.
