I downloaded an upgrade request sent to my note2. Since then my battery runs down very quickly. Any solutions ?
Chances are if the bug is widespread enough and an issue with the OS itself, they will quickly release a patch for it. At least that was my experience with Motorola in the past.
I myself have switched over to Cyanogenmod on my Galaxy Note II, I became fed up with Samsung's OS and the features they kept locking down on me (Their 4.3 update is what pushed me to finally switch, though I was contemplating it for a while).
I highly recommend doing this, but of course it's your choice. I've been running Cyanogenmod for over 6 months now, and loving it, its snappy, clean, open and my battery life is still close to what it was brand new. It's also very easy to install on a Note II.