I can't speak for others, but here's the issues I have with it.

Firstly, as you suggest, I dislike the notion of the government monitoring the Internet use of private individuals. Fortunately for me, I do not live in the UK, which is (to my inexperienced eyes) a country where this is a relatively alien notion. (Perhaps relevant: http://www.wired.com/threatlevel/2009/01/uk-approves-pol/)

Secondly, it essentially does an end-run around large chunks of what I like about the legal system (the parts with juries and lawyers and defendants-who-can-defend-themselves). I suppose I just have this quaint notion that if someone is demonstrably doing something illegal, you should drag them into court for it rather than mucking around with some ad-hoc, newly minted system for inconveniencing them.