For anyone who got one under a tree today for themselves or a munchkin... you may have experienced the following error code:
Error Code: 006-0803
Googling around, people are saying because of Christmas, that the servers are overloaded and that is the cause. I'm not too sure because I was able to get Netflix to work on one 3DS but got that error on another.
The only difference was I set up Parental Controls on the 2nd one. So when I removed them, guess what... I was able to start Netflix.
Initially, I just put Parental Controls on 3D image viewing so I just removed that but I got a different error code. When I removed ALL settings... it worked.
Not sure if that's a coincidence but you might want to try that to see if it helps you out... good luck and Happy Holidays.