I think I'm having the same trouble. When I export my animation to .mov, it leaves little traces of tweened symbols and looks absolutely shocking. I'm totally new to flash, so I don't know if I'm doing something wrong or if flash is dodgy when it comes to .mov's. I can't seem to find any answers online. Would love if someone can respond because I feel like I've wasted my money.
These is what I'm talking about 4 secs in: http://www.youtube.com/watch?v=_8d_68tMSDw
Is that what you meant about smoothness?
I'm having the same problem visible in the youtube link you posted. did you ever find a solution?
Unfortunately, no, I never found a solution. If you find one, please let me know. I'm quite disappointed because I bought Flash for animation creation. I'm now thinking of buying Toon Boom Animate as it seems to be a more suitable and intuitive program to use for animation.