I was doing a market research project for the city museum and art gallery of a town in the East Midlands (UK) about 10 years ago, and had the opportunity to talk to a lot of the staff. One of the things they told me is that most libraries, galleries etc have certain regular visitors who take an "excessive interest" in young, unaccompanied people - as soon as they came in they were monitored on CCTV, and if these people started following any kids around, the staff would either follow them very overtly, or, if contact was attempted, they would immediately ask them to leave. There was little else they could do, as the people in question were not actually breaking the law by walking around, or even by talking to the children. I don't know whether newer legislation will have further empowered staff or not. There were also junkies constantly shooting up in the toilets at the museum, something I've encountered as a regular occurance in every town centre venue I've worked in. Not really what you need, say, in the middle of panto. They'd even nick spoons from the cafe to cook the heroin in.

The problem is, as Lox pointed out, that there are kids everywhere. And paedophiles look for places where they can most easily gain access to them. The other thing to remember is that this is not a new situation, and I don't think there are any studies to demonstrate that actual ratios of paedophiles has shot up - our awareness of it has simply increased. So the danger is no greater than when we were kids, and as with all dangers, it needs to be kept in perspective. So yes, look after your kids when you're out in public, teach them about stranger danger, encourage them as a matter of safety to go places with several friends, and not to visit public toilets alone, as they are a much less attractive target in a group than a child on their own would be.