There are several scenes in which HAL's task to monitor and watch over, as well as his camera-eyes are mentioned. He uses camera to surveil the entire ship, and his "eyes" are everywhere.
Scene 1:
When their mission near Saturn is complete, the whole crew will go into hibernation and wait for the Discovery II to recover them, with HAL 9000 watching over them. They do not have the fuel or the supplies to get back on their own. This will never come to pass, as the mission goes another way entirely. (quote 1, p. 87)
Scene 2:
 Hal's primary task is to monitor the ship and the crew. Though the visual part of monitoring is not explicitly mentioned, it follows from the description. (quote 2, p. 93)
Scene 3:
Right after Poole is killed, Bowman is in a state of shock, but aware of Hal increasingly deceitful and hostile behaviour, as well as his lense eyes. (quote 3, p. 146)