[Comments from Lance]
Funny... I would say that the runtime itself is the very problem! For example:
1) It is incredibly slow.
2) There is no BCL. You have a few little built-in objects you can use, like sprite objects and xml parsers, but that is it.
As a result, it will definately only be capable of lightweight apps, definately not "smart client" applications... maybe we can call them "less dumb client" applications. If you are going to go through all the work of creating a Javascript based front end, why not just use DHTML? You get the same "everyone has it" advantages, except that you can make reusable DHTML components and encapsulate the logic in ASP.NET WebControls. In the end, the DHTML version will most likely give a better user experience as well, because Flash based UI components are so sluggish and don't blend in with the rest of the page very well.
You might say, "well, flash is cross-browser and cross-platform, so it is easier to support multiple devices than with DHTML". However, you must realize that a lot of cool Flash sites and apps require IE 5.5 running on top of Windows anyway, because the player isn't as really cross-browser as Macromedia would have you believe! So, given that your users are going to require high end graphics cards to view your site, and that you may end up having to require IE 5.5 on Windows or at least restrict to later version of IE and Netscape anyway, Flash may actually limit the audience instead of broadening it (the 98% proliferation is just the computers that have the plugin installed, not that will actually be able to run your app...and for Flash MX, the proliferation is only at 71.7% currently, and MX is required to do anything cool, so the numbers aren't that great). If you stick to DHTML, the DOM is pretty stable now in the browsers and there are plenty of js libraries to abstract the differences for you, so you are in a pretty safe place.
[1] Revamped Macromedia site irks customers
http://news.zdnet.co.uk/story/0,,t269-s2131698,00.html
PS: I used to be a big Flash fan. I wrote the SWFSource SDK, which enables Flash SWF support in third party applications and is generally considered the best choice if you are looking for an SDK for creating flash enabled applications (even before Macromedia discontinued their own SDK, we helped plenty of companies move their code from Macromedia's SDK to ours). So, I know a bit about the internals of the Flash format and have been around the block a few times. I still think Flash is a pretty cool tool, but Macromedia needs to make serious changes if they ever want to make any progress in the application development market.