[AT&T Galaxy Note 3 General] littlewierdo:
A couple of things...

When applying an update on Android platforms, the battery stats are usually wiped, this results in wonky battery drain and charging indications and it usually lasts a few days to as long as a week.

So, the short story is, see if it doesnt correct itself after a week.

On occasion, Android updates dont quite go right and regardless of how Google 'intends' for updates to go, 25% of the time, youll end up doing a factory reset after a firmware update (poor performance, new error messages, wonky power issues including higher than normal battery drain and slow charge rates).

Again, the short story is, after a week, if it hasnt corrected itself, Id suggest a factory reset, then give it another week to see if the battery issue corrects itself. Obviously, realize that if during that week you install anything new that this could affect your battery life. I personally try to keep my phone as stock as possible and disable as many stock apps that I know Ill never use (my Note 3 is at around 25 stock apps disabled and Ive only installed 15 of my own apps, none of which would likely have a negative impact on battery).

Best practices for the proper care and feeding of Lithium Ion batteries is pretty straight forward. There are alot of myths out there from Nickle Cadmium batteries that just dont hold true for our current generation of batteries.

1. Whenever possible, keep the battery charged. If you have an outlet available, plug your phone in, regardless of whether its fully charged or not.

2. Try to keep your battery / device in typical room temp environments (ie a temp range of 60-85 degrees F). Obviously, this isnt always possible but dont intentionally leave a battery / device sitting on the dash in your car in direct sunlight (direct sunlight can raise the temp by as much as 25 degrees higher than the actual ambient temp), dont put your battery / device on top of a heater, etc.

3. Drain the battery periodically (referred to as a full discharge*), currently, the rule of thumb is once every 3 months and re-charge with the phone OFF, once the phone has a 100% charge (use the volume rocker to see the current charge without having to boot the phone), unplug the charger, THEN boot the phone. This gives Android a chance to see what a full discharge and charge should be (and cycles the battery giving the electronics inside the battery a chance to see the same discharge / charge).

* Note that a full discharge in todays components is when a device shuts itself down when on battery power due to lack of power in the battery to continue operating said component without damaging the battery or the component any further. Do NOT continue to turn the device on after it shuts down in this manner without first plugging external power into the device as this will likely dramatically shorten the life of the battery.

The last rule is most important..

4. IMPORTANT! Use your device like you normally would. The above three are tips for making a battery last as long as possible but when and if your phone makes you change how you live your life to any degree of extremes, you've forgotten the point of what your phone is.

And I will now give you source information to the above, these guys are the battery experts...

http://batteryuniversity.com/learn/article/how_to_prolong_lithium_based_batteries

And lest anyone want to debate the battery cycling, here is a direct link to that information as well.

http://batteryuniversity.com/learn/article/battery_calibration

Read VERY CAREFULLY before you tell me Im wrong on this, batteries are a particular hobby of mine, I know enough to know what Im talking about.