Many thanks to Bright for sharing this link with us.
If anyone has problems with dropshadows on animations, this site has screenshots of the ideal settings to have.
On the screenshots you will see they have the Median box checked on the Colours tab. You may prefer to check the Octree box instead. If you're not happy with the result anytime, just change between Octree and Median to see which end result you're happier with.