Exporting to Video

I’m trying to export a Flash SWF to MOV that we are using for a 1920 x 1080 HD screen. When I export, most of the movie is smooth yet some of my tweens leave bits and pieces behind even though I’ve set the Quicktime settings to best quality (and I’m not undergoing any background activity).
How do I prevent it?

On another note, I once attempted importing a SWF to After Effects and exported video from there. Is this a better option?

Thanks in advance!