<p>I am an Ajax developer and I want to build a Flash application. Given my previous experience with JavaScript, what do you thing will be the easiest way to learn ActionScript and what are the obstacles I might encounter? </p>

Don't whatever you do start by buying Flash Pro. It is a designer tool and is really rather crap for developing code. By all means invest in it later, but it is a hindrance to coders getting into ActionScript; not an aid. I'd recommend getting yourself either
Flex Builder
if you can afford it, or an open source ActionScript IDE like
FlashDevelop
if not.
Then grab yourself a couple of books on ActionScript and/ or Flex and start reading. Also it is worth downloading any examples of simple Flash apps you can find that include code in order to learn how others do things.
Something to bear in mind when moving from JavaScript to ActionScript is that AS1 was very JavaScript-like, AS2 was less so, and there is little similarity between JavaScript and AS3. Thus if you have the time and inclination, try and pick up a cheap copy of an AS1 and AS2 book and skim through them first to understand the language's history. You'll likely get into AS3 far faster that way. Of course if you are aware of ECMAScript v4 (which will likely now never see the light of day), then you can jump straight to AS3 with confidence.