Overall I have to say that I'm pretty disappointed with the D4. I upgraded from the D3 and that thing was snappier and got way better battery life, even with 4g turned off.
Anyway, I've come to terms with most of the D4's quirks such as its horrible ability to switch between portrait/landscape mode. One thing I absolutely can not stand however, is when I pick up an incoming call: it will connect instantly but I will not be able to talk until the "call connect" sound does its jingle. This can be anywhere from instant to a 4 second delay.
Any ideas? As I'm writing this, I turned "call connect" off in sound options; have to wait for an incoming call to test and see if its the sound that's causing the delay or something bigger. I like having the sound though, it's useful when placing outgoing calls.