Problems with my Note 3:
I am getting the dreaded voice call quality issue that is rampant with Sprint owners - but I'm on Verizon.
My WiFi drops a lot but I only know this because I always see a fresh 'Established connection with WiFi' notice in my status bar. I have not seen any interruption when using.
If I'm texting a lot and typing a text and another text comes in, It freezes for 10 or 15 seconds, then I get a Verizon Navigator has stopped report box and once I get rid of that the new text comes in and I can continue with the text I was writing.
Home button does move around a lot (White model).
The latter three are minor annoyances. The first one is game over. The phone goes back. I might try a replacement but if that one does the same thing then I'm going back to my old phone until the issue is resolved which will suck because I REALLY like this phone!