Though Adobe AIR is a runtime for creating cross platform applications, it is very much possible to create an AIR application, that runs fine on - say, Windows and screws up on Mac OS X and Linux. Its up to the developer of individual applications to make sure that his/her application remains truly crossplatform.
Charles Ward from Adobe documentation team has put up an article on devnet highlighting areas that developers need to be careful about when they develop AIR applications. Go take a look.(http://www.adobe.com/devnet/air/articles/developing_crossplatform.html)