We added this functionality a couple of days ago, so it should be working. You can try updating your translators in the Preferences pane of Zotero and see if you can get DOIs from ScienceDirect. If not, please let us know. Thanks.
Strange: If the article is a chapter from a book on ScienceDirect the chapter's DOI won't be saved. I tried this with the following chapter: http://dx.doi.org/10.1016/B978-008044531-1/50453-X. Any solution to the problem?
PS: Is there by chance an easy way to get DOIs for all the articles I allready have from ScienceDirect but are currently without DOIs?