Sometime last year Fabio asked this question on his blog:
"Every day on the web new video related sites appear. Video sharing, video delivery sites or simply mashups, all Flash Video based. I'm very happy about this but there is a thing I can't understand and it is : why very often is video.smoothing property not used ? This is completely obscure to me because in my opinion a smoothed video is always better than a blocky one."

Of course he's right, video.smoothing is simple yet effective, once turned on your video will look a lot better. Take the following example. On the top you see the intro screen of a movie trailer with smoothing turned on, and on the bottom the same screen without smoothing (it looks bad because this video was scaled down quite heavily). Big difference, the top one looks a lot better.
Unfortunately smoothing (a property of the Video object in Flash/Flex) is turned off by default. To turn it on you simply set smoothing to true. Something like

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1myvideo.smoothing = true;
But what i you're using the FLVPlayback component? How does one access the underlying video object there? It's quite simple really if you know where to look. The FLVPlayback component uses the VideoPlayer object under the hood, and VideoPlayer extends Video and therefore inherits the smoothing property.
Say you have a FLA file (AS3) with an instance of the FLVPlayback component on stage and named it flvpb. You simply need to add the following code to enable smooting:
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1var videoplayer:VideoPlayer = flvpb.getVideoPlayer(0);
2videoplayer.smoothing = true;
Note that you have to specify an index when calling getVideoPlayer(), but if you are not dealing woith indexes then it should normally be 0 anyway.
Hope this helps, go use it and tell your friends how smooth you are.