My new Note was suffering the dreaded “Ice Cream Sandwich Power Drain” problem, but it looks like I have found a solution. You have to install the app “Cpu Spy” and confirm whether it’s going into “deep sleep” or not. If not, the most likely fix (unfortunately not permanent) is to power down, remove the battery for a couple of minutes, and then restart. Quiescent power drain (with phone and WiFi enabled) is now back at ~1% per hour.
There’s an excellent blog on this at the following URL: http://allaboutgalaxynote.com/how-to-solve-battery-issues-after-ics-update-in-your-galaxy-note/