I would not go for soft-shadows in an animation, because of rendertimes mainly.
My guess is that you have to increase atmo samples, since 16 is kinda low'ish.
I'd suggest to render a couple of frames with 32 samples and compare them to frames rendered with 16 samples.
If this doesn't help another issue might be the GI quality.
For a scene like this GI detail 1 should be sufficient, but you'd need some more GI samples for smooth non-flickering results, say GI samples @ 4 for example.
What are you using now?
So, first I'd try more atmo samples and then more atmo samples + GI samples.
Hope this helps.
Martin