I've also discovered today what a thirsty little beast the Note is while running satnav. I have a 1 amp car charger with the centre pins shorted together to force the phone to go into "AC Charging" mode, which it does perfectly well. However, over a 20 mile, 30 minute journey I was seeing the battery drop by about 1% per mile (every 90 seconds) whilst charging. That was with CoPilot Live Premium. On the way back I switched to Navfree, with pretty much the same result. I even have CoPilot set to dim the display in between turning announcements. On my old phone that make the difference between a solidly increasing charge and one that struggles to keep up. On the Note it was losing charge even with that feature enabled.
I'm going to need to be finding an alternate charger for the car, so recommendations would be welcome. I can't see a 2 Amp charger being a problem. The Note should take as much as it needs/wants, so long as the charger lets it have the juice it demands.
I would go for the official dock, except I'm told that it won't accommodate the Note whilst protected by a gel skin/case, so the official dock is a non starter for me.
Samsung Galaxy Note 3 running stock 4.4.2
LG G Pad 8.3 running stock LGE 4.4.2 (rooted)
Samsung Galaxy Note N7000 running stock 4.1.2 (rooted)
ZTE Blade running CM 7.2