Several sites present lists of potential remedies, but most seem to assume that the plastic is not widely-distributed and that most of the debris is large. What I have read seems to suggest otherwise, that the debris can be found across a large distance and also deep wihtin the water column. Furthermore, it sounds like most of the plastic has been broken down into small particles.

http://www.ecofriend.com/innovative-proposals-clean-great-pacific-garbage-patch.html