Same issue. 2 hours to fix/ resolve or it to just go away.
Got this to work (finally) though I'm not sure what ultimately cleared things up but I have a theory- see below.
First, I tried working with Apple Support. They were:
1) not at all familiar with this issue. "First I've ever heard of this."
2) strongly suggested that the issue was due to me not knowing how to use the side buttons
3) pointed out smugly, that not all apps can only be used portrait (hmmm...the native video viewing app, safari, iTunes etc. really???)
Ultimately I got the screen rotation to work through repetition of what I thought were the same steps: going into settings menu and after trying to set and unset the screen rotation "check." At one point I shut down my iPad down- while in settings mode and this seemed to work. I had done a number of shutdowns before- not while in settings mode- but they didn't seem to work. No more screen rotation lock issue! Hard to say if and why this did the trick. Could just be coincidence.
BTW- Apple care promised to get back to me. They didn't . Unhappy.