Sometimes I shoot at goats, and the killing cinematic runs, but the goat doesn't get hit. Sometimes the arrow goes through the goat and the goat keeps eating its grass. Is this a bug?

Some goats have super powers because they have also absorbed the souls of dragons and can use shouts....

But seriously, yes of course that would be a bug.
Although sometimes when the kill-cam starts the animal can still slightly move, making it look like they should have died but in truth you actually missed.

It went through the goat. I tried resetting from last save and shooting at different points, and none of the arrows did damage.

A goat killer hmm? You watch yourself now.