I'm self employed, so I have to monitor all of my own email and internet surfing.
Some days, I'm really well behaved and just stick to doing my work, but there are times when I have to threaten to take away my tea breaks if I keep sneaking off to do other stuff.
When my husband started working for his current employer, he specifically asked the MD if he could rewrite all of their blocks and monitoring because his co-workers were persistently finding loopholes in the current setup and not getting on with their work (he's really popular!)
If I need to get hold of my husband in an emergency, I email the MD directly, he'd be the one making the decision about him coming home, and he checks his email more often than my husband does.
I've no problem with it. If the staff aren't taking the piss or being inappropriate in the first place, then it shouldn't bother any of them, and those that are, you get to fire sooner rather than later!