The sequence of issues since taking the delivery on JAN 26th, 2016 :
1. Driver Assistance feature not available.
2. Charge port opening and closing by itself.
3. Again Driver assistance feature not available and also cruise control is disabled.
4. Key No Longer inside, car will not restart. This happened while driving the car today.
5. Charge cable is faulty notification every time the cable is plugged in.
I've seen 1 & 3 occasionally. These can be environmental (snow, gook, sun glare, whatever). Could be that sensors simply need calibrating. Keep in mind that this is still beta technology, celebrate when it works, report it when it doesn't.
2 - Too tight of a cover on your fob or something else hitting a button?
4 - If the fob for my LX570 is anywhere near my Tesla fob then neither will work properly. Fob for my wife's GL will also sometimes cause interference as will cell phones, etc. As others mentioned it could also be a battery.
5 - What cable are you talking about? MCU? HPWC? Supercharger? All of the above. Does it happen with a variety of charging cables or just one specific one.
Whenever something happens while the car is on you can press the voice/record button on the steering wheel, say 'note' then describe the problem. This will save your note along with telemetry for SC or engineers to analyze for resolving your problems. Usually this is only downloaded when in for service but I did once get a proactive call from Tesla that they'd noticed it and the issue would be resolved in an upcoming software release.
There's a lot of technology in these cars and some of it is pushing the envelope a bit. A bit of patience is still required but well worth it.