It all depends on how large the moon is in your photograph and how sharp you need it to be.
The moon takes a bit over 2 minutes to move its diameter in the sky. A 1.6 sec exposure will blur the moon by about 1/80th its diameter. In Alvin's magnificent photo, as posted here, the moon's only about 30 pixels (est.) in size. So, the blur is less than half a pixel. He'd have to be up around 3 seconds for you to see any blurring.
I'm not sure what you mean by the "movement" of the comet. It looks equally sharp to me in this photo. I don't mean this to be condescending, but are you perhaps confusing the fan of the tail with some kind of blurring?
pax / Ctein