@Fastcarve
You described the problem I have perfectly and I also had it since day one and as I mentioned I saw it with a friend of mine who has a galaxy note 3. Do you think this is a software problem that Samsung can solve with a future update.
Surprisingly enough a friend of mine who has the samsung galaxy note 3 phone told me he had the same problem where the screen dims and home button does not bring it back.
is this a hardware problem or software.
I have a similar problem and i don't have lecture notes. Sometimes while working the screen turns off and I can't bring it back by pressing the home button and have to press the power button.
It's a very strange problem and my device is not rooted.
My battery lasts around 6.5 hours and I am not doing anything heavy. I think samsung claimed something like 13 hours.
Please guys test yours and tell us how long the battery lasts.