Citing the "J documents" as part of a textual apparatus, on par with actual textual authorities, is probably the most amateurish aspect of the overall project (which at other times does reflect more responsible methodology), especially when the Society says that they "avoid overstepping the bounds of a translator into the field of exegesis" by only inserting "Jehovah" into the NT where the "Hebrew versions" do so as well. As if that makes it all right!
As cabasilas indeed points out, the insertion of YHWH in some of the Hebrew translations reflects an aim to identify Jesus with YHWH, which -- while exceeding the text itself which uses kurios -- is rooted in the actual christological application of Yahwistic passages in the OT to Jesus in the NT. The Society however has exactly the opposite motive -- to distinguish Jesus from "Jehovah" as two separate beings. As a result, the insertion of "Jehovah" in the NT actually obscures the actual christological application of OT texts to Jesus in the various NT passages, for the typical Witness will read "Jehovah" as referring to the God the Father only even tho in the original Greek kurios was used with both and NT writers freely applied OT kurios statements to Jesus, even if they originally referred to Yahweh. As a result, a JW can easily miss the whole point of a passage because he or she will think it applies not to Jesus but to someone else. A case in point is Romans 10 which becomes nonsensical when read in a way that does not identify "Jehovah" with Jesus.
The Society also does not limit themselves to quotations from the OT, as they imply. For instance, Jude 14-15 is not a quotation from the OT but rather from 1 Enoch 1:9, which had no name or title in this passage at all (rather it has the inflection for the pronoun "he").