I know the search function to the archived threads isn't the best, but if you search common problems, buying a used M35/M45 you can see some of the more "common" problems that members on here have experienced...that being said, I don't want to scare you into thinking you've bought a lemon (my car has really been awesome and quite reliable)
1. if the battery hasn't been changed, would make sure yours is pulling the correct cold crank amperage - many guys on here have experienced some serious electrical gremlin type behavior when their battery has gone bad even just a little bit.
2. Based on a recent post, make sure your key fob battery is new as well.
3. if you want your side mirrors to move when you put the car in reverse, these motors start to fail and the mirror will move down but not return back to their correct position.
4. AFS system in your headlights (they turn in the direction of your turn) these motors can fail too... recent post by a member here "what's this funny sound" thread
5. I recently had the "problem with filling the gas tank full, because the automatic gas pump shut off keeps activating" issue come up. fiddled with the angle that i was pumping the gas and the last few fill ups have been fine.
6. Luckily with the VQ motor compared to the VK (M45), you shouldn't have the oil consumption issue, but I would make sure that your engine hasn't been burning up more than the usual amount of oil or had any gasket leaks
7. a few fellas have had some problems with their heating/cooling seats as well - make sure you check all the luxury bells and whistles to make sure they're working like they should (voice commands, rear back up camera, etc.)
8. Bluetooth phone call sound/calls (there is a technical service bulletin to have a second?/new microphone placed so that sound is better
9. There are definitely some members that will dissuade you from choosing certain tires because of tramlining (the stock ones that came with mine, a 2006 M45 Sport model were sh*t...tramlining like crazy, lost traction with just a slight bit of moisture when taking off from stoplights and I wasn't mashing on the go fast pedal

)
that's a few of the items that I can think of....
congrats on the new ride and welcome to NICO!
Craig