http://www.craftster.org/forum/index.php?topic=177482.0
Is a tutorial for a fully lined bag. Making a lining is one way to encase all seams and prevent fraying.
With a nylon, I'd also experiment with some scraps and see if you can run fire lightly over the fraying edges and melt them into place. (Try this first over a sink!)
Finally, zigzagging the edges by machine or doing a blanket stitch by hand are the classic edge finishers.
Oh, and if you're having any leaking problems, use all polyester thread. I thought "wicking" was a slow process, but it's more like cotton/cotton coated thread is a pipe from one layer and moisture will go straight through.
