My experience writing a B2B sales app that runs on AIR is, yes, AIR is plenty stable both in the sense that it doesn't crash randomly and that the API is stable.
In fact, when compiling the application you explicitly set which version of AIR and Flash Player to target, freezing the API to a specific version. Further, AIR 3.x adds Captive Runtime allowing you to bundle a specific version of the AIR runtime with your application.
As far as working equally well on Windows and Mac (Linux is no longer supported as of AIR 3) I would say that the answer is "pretty much". I've found the Mac version to be slower than the Windows version but I haven't done any benchmarking so I can't say by how much.
Aside from that you just have to be aware of potential cross platform issues when writing your app. For instance, Windows and Mac OS application menus are somewhat different; when working with the file system be sure to stick 100% to the File API.