Paper (or indeed, any reasonably renewable and yet easily destructible) DVDs also bring the issue of software (and other IP) licensing to the forefront. We've all been in the situation where a software CD, DVD movie or audio CD simply won't play any more due to scratches, coffee stains or an inadvertent encounter with the family dog; a paper DVD would just be a much more chewable toy in that scenario. If, however, your software licence said something to the effect of "you don't own this software" (which most of them do) "but you can get replacements for the discs as and when you need them", then I'd be in favour of that. Sure, you'd probably have to pay a minor restocking fee, but that's got to be better than stumping up for the full retail price all over again.
The specifics on the creation process of the discs isn't yet clear, and as such I can only hope that, as appearances would have it, that the discs themselves are less damaging to whatever it is of the world's environment that we have left than producing a ton of plastic-based discs. Certainly, Sony's claiming that the discs will use less raw material than traditional optical media, and, certainly, there's always the hope that they'll be able to use a certain quantity of recycled paper in the production process. We can but live in hope.
Finally, there's one huge advantage to the paper DVD that comes to mind.
When I get advertising or software paper DVDs on the cover of magazines or through my letterbox, I can simply fold them into paper aeroplanes with "return to sender" written on the side. Who ever thought junk mail could be fun?