If you're serious about considering Ext as an option, you should really search and maybe post in their forums about others using Rails, I know there are quite a few doing so successfully. I just ran across this example that seems like a pretty fully-baked app doing just that, so it's definitely possible.
Without knowing exactly what you're trying to do, I think that saying Ext is "targeted towards business apps" is a fair general statement, in terms of the widgets that come with it out of the box. It's highly geared toward window/form-based Ajax apps. That said, Ext Core is very similar to jQuery and other core frameworks, and everything in Ext is built to be highly extensible (hence, "ext"). In terms of being able to build what you need off of it, it is very powerful and flexible. You can certainly implement a flash viewer easily, and there are existing plugins that will do exactly that.
Sounds like Toby had a bad experience with Ext, but many other people enjoy it and find it very natural to code in. The syntax definitely has a Java/C# flavor to it in some ways (although it's really hard to directly compare any JS framework to a static language), and it has roots in YUI (which is even more verbose). For someone coming from C-ish backgrounds, it will likely feel very comfortable. If you're more used to Python or Ruby or something else, then it might not be as enjoyable, I don't know. Something you'd have to try for yourself.