Well my youtube automatically updated, and in playing around with the app I found a workaround. If I enter full screen in portrait mode, the controls work, and then I can flip it to landscape and the controls are still there.
I didn't realize what forum I was in. This definitely appears to be a bug specific to Samsung tablets. I reverted to an earlier version of youtube and if works fine.
What device is this happening on? YouTube works fine on my old Nexus 7, but my brand new Samsung Galaxy Tab Pro 8.4 is missing the controls in full screen. My Google search for this problem led me here.