My D4 has been acting hokey over the last 3 or 4 days as well.
Something is causing the screen to stay on until I press the power button to turn the screen off. If I have a text message, and set the phone down, I can watch the screen flicker and go from dim display to normal brightness when it should turn the screen off and continue to this cycle.
Also, while on a charger (Moto brand) I have it set to keep the screen on while charging because of the docks that I have (all moto brand). But if I press the power button to turn the screen off, I am getting the Droid notification sound with nothing incoming.
Of course I am rooted, so it doesnt look like I will be taking this back to Verizon for service.