Just some notes by way of clarification. I've have a wireless network with several devices attached. My iMac computers conntect wirelessly and they work perfectly fine viewing and buffering videos using Safari. But, things just don't work using the mobile devices. I've tried m.youtube.com and the newest YouTube app - both give the same resutls.
As a suggestion, I tried clearing all Safari data and for the first time in recent memory, the video did cache, although very slowly but I was actually able to watch a video for the first time in a long time. However, I lost all my history and data to clear everything out.
As suggested, I tried m.youtube.com, instead of the YouTube app and I can login and search for videos. But when I select them, they are very slow to load, and seldom buffer almost as if the internet connection is very slow but I know its working great on my iMac. I also verify that my speed is adequate using a bandwidth tester on the mobile device.
I've also tried other browsers like Chrome with no success.