Small update: this occurs on iPhone 4S and 5 running 6.1.3 and an iPad 3 also running 6.1.3. About 1 out of every 10 videos I click on will play. I'm just browsing through the popular videos.

Wondering if anyone else has had this issue as I've only found one thread on google with anyone else experiencing anything similar. Cellular data off (poor coverage at the office, done to save some battery) running on corporate wifi. I have full access to everything on youtube/netflix, etc...