It seems to me from the Google webmaster article linked by Guardianangel that the worst that happens is that the duplicates just don't get shown in those results. But of course they are still getting seen by people who look at the article directories they're on, as well as the sites that have published them. I assume the backlinks still help a little too for SEO.
I think that if there was any real problem in submitting to many directories, then you wouldn't submit to even one of them. The whole point of doing that is for your article to be duplicated at many other locations, after all.