I have a shared photostream with 7 people subscribing to photos. Now that iOS 7 is out, I was eager to try and share a video. I captured one using my phone and edited in iMovie on the phone, exported to camera roll in 720p and then put it on my shared photostream.
I can play the video from my iPhone that uploaded it, but not from my iPad. There's just a spinner that never disappears. My subscribers have the same issue, regardless of phone/iPad.
The clip is 18 seconds long, by the way.