This is an issue with the way objects are exported/imported.
It sounds like the imports are being done as Bitmaps, in some way, which explains the jagged edges and the horrible scaling - we often have the same issues!
You should be able to export and import as a vector graphic (SVG) and that should maintain the effects.
However, these effects tend to give pretty bad performance within the Flash Player (except on the desktop). Just a word of warning!
One way is you can export as a SWF and import that object - it should maintain effects. You WILL need to rescale this SWF, though (just set the .width/.height properties when you include it in your code and you're away).
Other than that, we try to avoid using any fancy effects and, if they are needed, build them onto the asset when they are created.
One other big one that we noticed, is that PhotoShop's "Pass through" is not the same as using the alpha channel within Flash/AS3 - or at least, it doesn't give the same visible effect. (I know the OP was about Illustrator, but I would wager there are similar problems with effects from other applications).
Sorry I can't be of much more help :-/