Since upgrading to Lollipop on my Note 3, I've had battery drain issues. I've done a factory reset, turned off applications that I don't use and still have the same issue. Before the update, I could go all day and still have 75-80% of the battery left. Now I'm luck to make it 2-3 hours before hitting 75%.
Noticed that WiFi keeps dropping and reconnecting at random times. We have three different WiFI SSIDs at home and I've seen my phone connect to one, then sometime later drop and connect to one of the other SSIDs. Didn't have this issue with KitKat.
I did call Verizon over the weekend about the battery issue. I was just told that its a new OS and battery usage most likely changed. I'm not buying it.