Not all devices have had problems with the 4.1.2 update. Have you tried a system cache clear on the phone yet?
Power down phone
Hold volume up/down & power simultaneously until you see the Boot Mode Selection Menu
Use volume down to navigate to 'Recovery', use volume up to select
Should see screen with triangle and exclamation point next to an Android
Press volume up/down simultaneously to go into system recovery
Use volume rocker to navigate to 'wipe cache' and use power button to select
Once finished, use volume rocker to navigate to 'reboot system now' and use power button to select
This won't erase any data or change any settings, but it just may help clear up some of the issues you are having. Apps that are not updated may also cause problems, so be sure all your apps are up to date.
My OS (4.1.2 on Motorola Droid 4) is 33% of my battery usage, going 9 hours + and at 70% left. Screen is 35% - it varies but it's not been 90% and I get many hours of use....