Thanks for the tips. My Flex test project's size is 1000x600 and I made 2000x1200 size image. It looked nice when it was resized to 1000x600 in the beginning when I ran the project. Right after I resized the swf player either to smaller or to larger from 1000x600 the image looked bad. On the other hand when resized to 500x300 the image looked good.

I am doing the full screen resizing like this:

stage.addEventListener(Event.RESIZE, scaleAgain);

Is this the same as Stage.onResize() event?

Does the description above tell you that the smoothing would do the thing?
How can I use bitmap smoothing in Flex? With the bitmap filters perhaps?