He was unaware of the police('s) watching him.
Czy apostrof z "s" może tutaj wystąpić?
Unaware of the police's watching of him, (=unaware of the police's surveillance of him), or—which would be better—unaware of being watched by the police.
The gerund "watching" is a noun and needs "of."
The participial "watching" doesn't take "of": The police, (while) watching him, were stuffing themselves with another batch of dunkin' donuts.