Looking at the apps available:
1) Dash Command is $50 in addition to the cable. Most, if not all, of the information shown on the screens in the app store is N/A to the Leaf. Things like fuel trim, transmission gear, engine RPM, and so forth. It might report on a few things that we'd find interesting, but it is very difficult to tell if it will report on ANY of the Leaf codes without spending $150 or more.
2) ReadyLink, which is advertised as a "are you ready for inspection" tool (not a generic scanner) is $4.99. Hmmm... $4.99 for something that is based on scan codes but more limited in functionality? No thanks.
3) GoPoint, and BT1 are at least free, so we could check them out. BT1 is for their BlueTooth scanner only, so that's out. The sample screens for GoPoint seem oriented around gas vehicles as well, but perhaps there is some generic code reading stuff. Maybe.
I downloaded GoPoint and there appears to be no Demo mode. It wants you to create an account, but you can skip that. Attempting to configure the scanner crashes the app. Yes, I don't have the scanner plugged in, but it should say that, not crash. Not a good sign... Attempting a quick scan does say that there is no scanner attached.
So, it is impossible to tell how flexible the app is until you buy the cable. Another bad sign.
If I had an ICE car, I'd consider one of these. For a Leaf, I'd pass at the moment.
These guys look interesting: http://www.autotap.com/product.asp" onclick="window.open(this.href);return false; Although they don't run on a phone...