When I was having a second key programmed, the locksmith blew the ODB fuse (unknown to me) and that light came on. Of course I couldn't use Leafspy without the ODB working. However, I checked all fuses and found one blown. Replaced it and the ODB worked again and the light went off.
Re: wifi LeafSpy Pro:
I had problems connecting through wifi as well. If I put the iPhone in airplane mode, turn on wifi, then select the ODBII, it works.
The key was putting it in airplane mode to turn off the internet.