Regarding the battery life:
1. Google removed the factory images of 4.2.1. Many believe this is due to the bugs in it (there is a deep sleep bug they've admitted to) and the fact Qualcomm believes their hardware drivers need to be updated (see below). This also implies that an update is coming soon.
2. XDA has discovered that Qualcomm locks the processor cores to 1ghz whenever you touch the screen and leaves it there for about 3 seconds before allowing it to throttle down to about 300mhz. This means that even when you're just scrolling or tapping or doing any other low-load tasks, the processor is still running at a higher clip. Worse yet, when you stop touching the screen, it takes a few seconds to throttle itself down. People have found that using a rooted device to cap the processor at 980mhz exponentially improves battery life, and the phone immediately throttles down once you stop touching the screen, instead of lingering there. Many have gone from 3hrs average screen time to 5hrs+ with heavy usage -- with just this one minor tweak.
3. Apparently, Qualcomm is aware of this throttling issue, and they plan to update their drivers to make them less aggressive.
4. Points 1 and 3 are speculation, so don't kill me if they don't pan out.
