If your child is watching gore vids on the internet then the solution is to sit down and have a very serious talk to the kid -- not to rely on a technical solution to prevent it.
It’s pretty much impossible to fully block whatever you consider negative. But you might be able to reduce it or make it less accessible.
Monitoring is a whole other matter.
Unless you rely on catching them by accident, that seems to reintroduce the need for monitoring that we were avoiding, so I replied asking how we're supposed to know such things without it.
Monitoring is related. The whole subthread is about avoiding it.
For what it's worth, I couldn't even monitor all my teenager's Internet traffic even if I wanted to. We have had the "there's a lot of wierd stuff on the Net" talk, and there has been other kids at school who apparently MMS'ed some pretty bad stuff to the other kids, which resulted in a very productive discussion about peer pressure and the importance of being responsible.
I believe that approach is better than trying to control everything. Otherwise you'll simply end up with a bunch of kids in a small bubble that bursts when they move out, and then the World will simply come crashing down on them no matter what. It's better to prepare them for what's to come.
Also if kids are comfortable talking to you about what they do because parents are understanding rather than judgemental ("how dare you watch X" etc) then they're more likely to tell you if they do come across something like that accidentally.
(My kids are <2 and <0 right now, but I teach teenagers about technology for a living and kids self-report dodgy stuff all the time.)