So in an effort to figure out what I can do with different devices, I came across this VERY useful document on Adobe's site. It essentially outlines the features of AIR that are not available across platforms and tells us, of those features, which are available where.
For example, I suspected, but did not know that the Encrypted Local Store would not be available on mobile devices (yet?).
If you plan to develop for multiple device profiles (Desktop, Mobile, TV) then you need to take a look at this: