Well I must sound like a bit of a bossy cow but I have no problem whatsoever telling other people's kids how to behave in my home! IMO, if their own mothers can't be bothered to enlighten them, then I'm more than happy to. This has only become an issue in the last few months as DS is 2yrs8months now, but with some of his friends I really have to be vigilant.
If an incident occurs with no adult present to witness it, I always question all the children in the same way as to who was responsible, and usually get the answer (I find they can't lie at this age ). Once or twice the mother of the offender has refused to accept it, or insisted it must have been "an accident" (yeah, I'm sure your child scribbling on my walls in orange crayon was just an accident!), which has left me quietly fuming. I certainly wouldn't hold back from loudly saying No to any child I saw doing something naughty, but it infuriates ne when their own mum sees and either admonishes them in such a wet, half-hearted way that they know they can get away with it again, or worse, just acts as though they didn't see at all. I find this is the most common response actually - if I didn't see it, it didn't actually happen, sort of thing.
I still see my NCT group each week, and while I like to see them, I am finding it increasingly stressful having them over to my house, as all I do is police the kids while the mums stand around eating cake and drinking tea. A couple of them are so badly behaved, I just don't want them in my house any more (currently trying to get out of this, but not sure how!)
Just so I don't sound too draconian, my own DS is by no means angelic, and I frequently have to "guide" him, but rarely have to actually punish him and have hardly ever smacked him. He just knows from the expression on my face what is and is not acceptable behaviour. It amazes me how some other mums I know talk about their children as though they are some kind of perfect being, never discipline them, and then look askance at you when you tell the child you don't really want sand all over your garden/crayon all over your walls, thanks very much! My mum's a primary school teacher so I know how popular these kids are with the teachers when they arrive at school IYKWIM