Carolyn, I think it depends on the final destiny of the quilt. Is it a drag-around quilt for a child? I wouldn't worry about it. Is it headed for a show? The judge will not like seeing thread shadowing through, you you will need to deal with it. Then there is all that middle ground where it's just a judgement call.
If the quilting has already been done, you can use a size 14 crochet hook to fish out the offending threads, or get a really nice tool for that task here:
http://www.frederickchill.com/sales_pokenpull.php
For future projects, you might consider starching your fabrics before cutting out the pieces. That really helps to control fraying.