The other day my daughters were watching a movie on one of the kids' channels on TV. Based on what they had told me about the movie (which was all that they knew from looking it up online) it sounded like it would be okay. But after it was over and they came to tell us about it, we discovered that there were elements of the story that were not necessarily things we would want them to be exposed to. In fact, if we had known about it ahead of time we probably would have told them not to watch it.
However, I was not angry with them nor did I get angry with them. Instead, I used the opportunity to discuss with them the issue of discernment and being able to determine whether something was appropriate for them based on what was contained in the program. We discussed specific examples of other programs we have told them not to watch and why we found them objectionable.
Our goal is not to police everything they watch or read. Rather, it is to help them to develop discernment and to understand what worldviews are being represented in different programs. Often, we find that material that is theoretically targeted towards kids our age (they are 10 and 9) has content that is really more suitable for older children. We've had to work with them to help them understand that they need to be aware of the messages that are being relayed through media and be able to understand the agenda behind the entertainment.
Developing discernment in my kids has not simply been about telling them what is right or wrong. Nor has it been to say "this is okay" or "this is not okay". Often, we have to go beyond simple right and wrong and explain the reasons why we object to something. By explaining this to them we are helping them to make wiser decisions on their own. That's really the point of training a child in the way they will go: so that they can make wise decisions when they don't have Mom or Dad to make them for them.