Yep, always use the fast idle lever when starting from cold and keep it on a little bit until your engine is up to temp. Works very much like the old chokes.
+1 for the idle/ choke. Start it (on the bike, like yuu pointed out), get it idling around 2k rpms (this should avoid building up any back pressure and get the flow going) and let it warm up, as it becomes warmer the revs will rise, just nudge it down. I don't always wait till I see a temp reading (comes on at 126f) but I'll still let the bike idle higher at lights and stops etc.. Once you get the temp. you're good to go, close the idle lever and let rip. I've had mine stall on me a few times, these bikes seem to like to run hot.
Secondly, your neutral problem sounds familiar to me, I've had it happen a couple of times to me and I've heard of it happening to other people (never on my duc) on all kinds of bikes. I think you have 2 things going on here: 1) You have a brand spanking NEW bike which requires a break in (not just for the engine but for most moving parts) you'll find things will smooth out once it gets a few more miles on it. 2) The false neutral is a common problem - where the sensor is as far as what stage of the circuit could have an effect on weather the bike starts when the neutral light is on, the bike thinks it's in neutral because the sensor is triggered but really it somehow slipped in to gear, or as was mentioned by yuu already, it was just teetering on the neutral point and the starter force may have kicked it down/ up in to gear.
I've had problematic neutral on a couple of Japanese bikes, literally the thing wouldn't find neutral, it was either first or second, I found If I feathered the clutch a little while shifting for neutral it would go in no problem. Anyways..
This is probably the last thing you want to hear but - It's probably not something to worry about, get out there, enjoy your new beast and put some miles on it. If it keeps happening, that's when you know something isn't right, probably something simple that a tech will pick up on straight away and you'll be covered by warranty - plus, they should be giving you as much attention as you need as a new owner, I would take the bike down there with no warning if you're worried, I'm sure one of the techs will spend a few mins talking with you. Sorry for a long winded response! Congrats on your new bike!