I doubt you see this in AE.
It's probably due to the media container & codec to which you exported. MP4/H.264 is notorious for this. In AE, you can an a tiny bit of noise on an adjustment layer. Really. It helps.
If there's no joy using it, I recommend a better codec. Plus working in 16 or 32 bits in AE. Not 8.
KGAN (CBS) & KFXA (Fox) Cedar Rapids, IA
ive had this problem before and it wasnt a codec problem...but i cannot remember quite how i fixed it..Maybe you could pre render with alpha png sequence and add the drop shadow to that?..do you have any adjustment layers or any other effects on the element layer..try turning them off one by one and see if it goes away.