When I'm not actively using the network, I usually turn off Wifi, Bluetooth, and Data. Since upgrading from Android 4.3 (stock) to 4.4 (OTA update from my carrier) I notice two things:
Battery life plummets. The device could be fully charged at night, but when I wake up it reads < 20%. This with Wifi, GPS, Bluetooth, and Data all disabled, and no applications actively running!
I often get a small system popup at the bottom of the screen that says something to the effect (translated) "Could not contact the network. Please try again when your have network access". This looks like a system popup, especially since it is in my local language.
Looking in the Network Usage area, I see nothing suspect. The largest user is Google Play at 1.89 MB, below that Skype at 804 KB, everything else is below 500 KB. Looking in the Battery Usage area, I see "Operating System Android" at 33%, "Screen" at 23%, and "System Android" at 13%. Before the 4.4 update, only one of the two "Android" listings were shown (I don't remember which) and it was in fact well below the screen usage (i.e. the screen was at the time by far the most battery-hungry app). Note that all three of these names "Operating System Android", "System Android", and "Screen" are translated from the system locale language.
Unfortunately I cannot peg the problem on the 4.4 update as during the same day I did install 3-4 calendar apps to see if any of them provided a better experience than the default app. I have since remove all of those.
This is on a Samsung Note 3. I currently have the following applications installed: Ankidroid, Appops, Earth, Waze, Skype, SatTrack, AirDroid, Opera, ES File Manager, JuiceSSH, Firefox, Galaxy Call Recorder, Pocket Planets, Widget Locker, VimTouch, LastPass, Translate, Dolphin Browser, XKCD, Podcast Addict, Swype, Swiftkey, Motion Planet, Read Later, DCentral1. Podcast Addict is set to never automatically check for podcast updates, though XKCD does automatically check. I don't use Swype's Living Language feature that was recently noted as a source of battery drain and network usage. I have tightened down some apps' permissons via Appops and later with DCentral1. Additionally, there have been other apps installed and since removed from this device.
How could I further troubleshoot the battery drain issue? Should I leave the network on to see what will use it? Additionaly, how could I check which app is trying to use the network when I get the "Could not contact the network. Please try again when your have network access" popup?