I actually had this problem (playback Error 80070005) when I tried downloading or instant stream on Zune. Never had problems with netflix or watching previews on Zune. Boggled my mind. I think the issue is with transferring profile data from hard drive to new hard drive via the xbox data link (cord). Somehow there is something zune doesn't like about it. Here is the fix and I tried it twice and it worked. I have an arcade console with a 120gb hard drive. What I did was moved all my saved files, profiles, etc to the Arcade's already existing memory card. I then formatted my hard drive (yeah I know, very scary but make sure you have everything transfered over). once formatted, I recovered my xbox live gamertag and it asked me to update to view video marketplace and I said yes. That was it no extra updates. I played a free clip from the new movie Sherlock Holmes (not the preview but an actual clip that you had to "purchase for free") and it worked!!!! I was watching zune movies in no time.
I did however have to redownload all my game add ons which was a pain but oh well.
Im not sure how to do this without the internal memory on the arcade console but I know that transfering hard drive to hard drive gave me the error to begin with so you might try getting a memory card for it (not a thumb drive, that doesn't work)
also if you don't want to reformat your drive you could always download the movies using your computer and then share the folder so your xbox can access it (it was kind of a pain to download then wait as opposed to instant streaming)
Hope this helps you