My first thoughts.
IT's job needs to occasionally monitor what websites are being accessed, or just outright block certain content: porn, gambling, hacking... whatever.
Management's job is to make sure their employees are doing their job.
Part of IT's job can also be providing applications and reports to management to assist in ensuring employees are doing their job. Pretty common practice. Managers can also come to IT and ask for help determining if an employee is misusing corporate resources. It doesn't hurt to have tools available to honor such requests. The ethics question isn't as much about the tool as it is about the usage of said tool. Many times, simply possessing the ability and informing employees about it is enough to ward off anyone who may be tempted to do things they aren't supposed to.
For the OP, some good suggestions here on monitoring software. To add one, I've used an IM/corporate messaging solution called "e/Pop" that included remote desktop monitoring, and a tool similar to a remote taskmanager that would list running processes and open windows. Used in conjunction with web monitoring software, you could easily get a feel for who was continuously violating policy via web usage reports, and narrow in on the problem through the remote desktop monitoring.