When doing research for this blog post the top concern I kept seeing is keep your computer in public places. Keep your computer in the common area of your house. This makes it easier to supervise your children and what they are doing.
Be involved with what your kids are doing. If they are playing a game with the others online you need to join and play too. Know what is going on at all times. Don't assume that they are dealing with other kids.
What about youtube. You gave your child permission to watch some silly video on youtube. Have you looked in the history to confirm that was all they watched. Even when you completely trust your children they are still CHILDREN! They have natural curiosity. That curiosity can lead to things that are not good for them. Check out this forum thread where that happened to a mom and totally surprised her that it was her daughter who was looking at in appropriate things on youtube.
I recommend you that you install a program on your computer that will help you watch your children and keep your children safe. There are programs like Net Nanny and K9.
What do you do for internet safety in your house? I would love to hear what you do. Might be an idea I could implement in my home.