What do you like best?
Flash allows development for 3 of the 4 most common targets (desktop-web, desktop-app, mobile-app)., Unfortunately the one not supported is becoming a biggie - mobile-web - and leading to the demise of Flash.
As well as rich media, also supports complex web applications via the Flex framework.
What do you dislike?
Not well supported for mobile web.
Flash is being superseded by HTML5/JS in one of its two last two big areas (rich web advertising), and is now only really used for online games and some mobile apps.
Senior Flash/Flex developers are now rare (we spent 6 months trying to get one in January 2015, and have essentially given up).
Recommendations to others considering the product
What business problems are you solving with the product? What benefits have you realized?
I am a senior Flash/Flex web developer, having worked with Flash since the late 1990s, and having published 20 books on the subject.
Flash is still the fastest way to create compelling rich media and Web applications, but lack of support for mobile-web has killed it for most new projects except mobile apps (via Adobe Air).
Having said that, Flash based authoring that is then exported to a HTML target (that runs as a HTML5 canvas object) is still a viable option for high end interactive web content such as social gaming clients.
I currently still use Flash/Flex in my day-day work, but it is finally beginning to ramp down and am moving over to HTML5/JS solutions