Flash has two basic uses, animation and web content. The two areas see some overlap, but generally, the two camps of Flash users, animators and web developers, have very different needs and live strange parallel lives. Initially, the animation was the primary purpose, because video was basically impossible to stream at that point, so if you wanted to make a web cartoon, you needed a special lighter weight format that would load before the user died of old age. Also, scripting in Flash 1 through 3 was worse than being suspended over a pit of rottweilers by your arm pit hairs. As it improved, though, actionscript become more useful, and as web connection rates improved and streaming video became more possible, content delivery became the primary use. Nowadays, if you've got an animation, it makes just as much sense to convert it to a traditional video format and distribute it that way.

Flash has many problems in both areas it is designed to function in. For content, any web developer in /r/programming will be glad to write a lengthy dissertation on the many of sins perpetrated by Flash. It's closed source and doesn't obey the standards, limits SEO, and websites made with it tend to be very unintuitive and ridiculous, even if they look pretty. There are more, but, as animators, we don't really care about these.

In animation, due to its vector graphics, many artists find it unintuitive and get poor results. Vector graphics can indeed be limiting, but they do lend themselves well to a distinct style of animation that can, as has been shown over the last couple weeks here, look fantastic.

The bigger problem for me is that it just doesn't lend itself very well to higher level animation. Look at a program that is absolutely dedicated to animation, like Maya. You have so much more control over your work it doesn't even begin to compare. Support for image sequences is iffy, controlling tween graphs is a late coming feature, and, worst of all for me, exporting the work into anything other than a .swf file is an exercise in frustration. The fact that you basically need to have a third party app to do so is beyond ridiculous.

Even with these faults, though, I still use Flash for what little 2d stuff I do these days, mostly because I know it so well. Flash was the first animation I ever did. It was so easy to get into, and what you see is what you get (for the most part. Scripted effects don't show up until you export, but that's a different story entirely). It's great for beginners, but if I could draw as easily in Maya as I can in Flash, I would never look back.

In general, I think Flash is being left behind by the inevitable march of progress. Animation can be done with better, more focused programs, and content will be more and more delivered with canvas and video tags in html.