I wondered after I read the article whether they had accounted for the possibility that those who became fully bilingual were already smarter to start out with, and that's why they mastered another language so well. Even under similar circumstances (like living in a foreign country, or having parents who speak different languages), I've seen people who indeed become truly bilingual (which doesn't mean just knowing two languages, but knowing both almost equally well) and I've seen those who pick up a practical knowledge, and even those who know little or nothing of the target language.
Another important issue with practical ramifications is whether in fact the benefits only apply to those who learned the second language as a child, or to those who learn a language later. They do in fact mention that bilingualism may forestall the perceived onset of dementia, but it isn't clear if this would include learning a language later in life.
Another article on the same topic, from the viewpoint of neuroscience, was published last year in the Times and can be found here.