Java is probably still the best cross compatible runtime, but it comes with its own set of problems. If you are looking for something that can cross OSs, and work and out of browsers, Flash targeted rutimes are a very good option.
Drawbacks to AIR are its deployment model, the difficulty in getting Enterprise to adopt it as it is an installed product which makes changes to the registry. Download and run jars have the advantage.
Positives are its deployment model, it's easy to stick up a new version and have people update automatically.
I don't think there's anything Unique to AIR other than Adobe's commitment to the runtime. No-one else seems to be fully committed to supporting Java / Silverlight / AN other.
I'd expect AIR to increase it's market share against Java for off the cuff applications, and increase its share in other spaces. AIR for Android is a great example, virtually the same set of code can be deployed on the desktop or on the mobile.
The only danger to Flash / Flex / AIR is how much traction HTML gets in the forthcoming years. However the browser is becoming a bit of a kitchen sink development with everyone trying to use it for everything, and the browser wars putting the kibosh on cross compatibility.
I think it'll wash out eventually. People will come to the same conclusions with HTML as we came to with Flash. Don't build a website using Flash, don't build an RIA using HTML.
Conclusion? AIR is an excellent runtime, well supported, and with promises of more enterprisey support in the future. It stands up well to its competitors, and offers plenty of scope to expand off the desktop and into the web if required.