In the early days, some authors worried that open access would increase the incentive to plagiarize their work. But this worry made no sense and has not been borne out. On the contrary. Open access might make plagiarism easier to commit, for people trolling for text to cut and paste. But for the same reason, open access makes plagiarism more hazardous to commit. Insofar as open access makes plagiarism easier, it's only for plagiarism from open access sources. But plagiarism from open access sources is the easiest kind to detect.
(From Open access and quality written by Peter Suber, SPARC Open Access Newsletter, issue #102, October 2, 2006.)
In fact, plagiarism is diminished as a problem. It is far easier to detect if the original, date-stamped material is freely accessible to all, rather than being hidden in an obscure journal.
(From the Open Access Frequently Asked Questions, DRIVER — Digital Repository Infrastructure Vision for European Research)
It is easier to detect simple plagiarism with electronic than with printed text by using search engines or other services to find identical texts. For more subtle forms of misuse, the difficulties of detection are no greater than with traditional journal articles. Indeed, metadata tagging, including new ways of tracking the provenance of electronic data and text, promise to make it easier.
More information: see JISC Electronic Plagiarism Detection project