Jeff,
I've had a similar experience to Behl. I've had some successes with Parafilm, certainly, but also some failures due (I think) to cracking of the product and dessication of the scion. As an example, I did some grafting about two months ago on my cherimoya, using parafilm, that only broke dormancy in tha last week or so. I had given up on them, but the parafilm held moisture in the scions all that time, and they were still viable when the tree began to push new growth. On the other hand, earlier in the spring, I did quite a few stonefruit grafts, and only had 50-70% success. When I inspected the failed grafts, within about a month of performing them, they had already cracked in the sun. My guess is that success with Parafilm is dependent on not overstretching the tape.
James