While discussing this topic in a discussion group, Michael Senders interjected some helpful information:

“The Greek word in question here is θεοτης (here it appears in the genitive case, της θεοτητος). There are two big issues with the JW rendering in this verse. 

1) θεοτης is a noun, sometimes used as an abstract noun. Their translation “the divine quality” would make “quality” the noun, and “divine” an adjective. θεοτης, though, describes not a quality being singled out from many qualities, but the “state of being God (BDAG).” The noun is a derivative of the noun θεος, and contains everything that is contained in θεος. To be θεοτης, especially in a Jewish monotheistic setting, is to be God himself. 

2) The second problem is Paul’s polemic here, demonstrated in the preceding word πληρωμα and the following word σωματικως. The former is a technical loan word from Gnosticism for their pantheon of deities, “the Fulness.” The latter word, σωματικως, also speaks against the Gnostics for many of them were docetic as well. They denied that Christ had a body, that he only seemed (docetic, from δοκεω, to seem) to have a physical body. So, Paul’s use of Greek terminology here represents a polemic against Gnosticism in that what he’s saying is that the totality of what it means to be a god, what the Greeks called their Pleroma, is well-met by Christ, and done so in a physical body. Anyone reading that with Greek eyes would understand that Paul was confronting the gnostic beliefs. NWT rendering undermines that, and opens the passage up to gnostic interpretation in its original context.”

He also posted:

“Their problem with the whole issue of “divine,” in any context where they engage it is that they take the word as equivalent to saying something like, “This chocolate cake is amazing, it is truly divine.” The problem is that the word is never used like that anywhere; the point of the word is to attach the meaning of theos, “god,” to a person adjectivally. To be “divine” in the sense that theotes requires it is to be “everything that God is.”

Check out Michael Senders and his Pressing On! Podcast, found at http://www.soundcloud.com/pressingonpodcast