IMO, the problem is developers. Because of Flash's origins as a tool for designers to make animations, most ActionScript is atrociously bad. The lion's share of Flash is created by people who really don't know how to program. When you have a community where knowing what recursion is marks you out as above-average, it's understandable that the core technology gets a bad rep. The problem is self-reinforcing, as good developers want to use the new shiny HTML5 and don't want to tarnish their CV with Flash development.
A huge spectrum of really high-quality web apps are reliant on Flash. Streaming video is the obvious application, but projects like SoundManager2 are still reliant on Flash for audio in HTML5 apps. It's a very nineties word, but Flash is still the bottom line when it comes to multimedia. Products like Google Street View or Turntable.fm just aren't plausible without Flash and won't be for the forseeable future. Given the glacial pace of the W3C on HTML5 and the likely slow uptake of newer browsers, we're stuck with it. I don't see that as a wholly bad thing.