The cog where the bird has her nest normally has a shaft and raised hub. When the rope breaks and the cog starts to spin, the shaft and hub are gone. They reappear in the next shot, but the shaft-less cog is seen in some shots soon after.
The reflection for the ducks is supposed to be down center of screen, like the windmill's reflection. Therefore, the ducks reflection is not missing, but off the screen, down and center.
In the opening shot the mill is reflected on the pond. The ducks swimming in the pond, however, have no reflection.