The problem is not being filmed, when the recording is used in small circles.
The problem is when it's published for the world to see.
As a rule of thumb, for my children at school, I refuse any use of their image if it's not for something that was already possible in the eighties.
Publishing school party pictures and videos for the whole world to see was impossible in the 80s, I thus don't allow it and if it happens, it's an invasion of their private life (as per Belgian law at least).
Hanging on the school walls some pictures of the classes, or children, doing some activities: that's OK, it could already be done in the 80s and might be useful for the school community.
Publishing these in a printed yearbook: I accept. Publishing it on the Internet in electronic format: this was not possible in the 80s, thus I refuse.
I think this time strikes a nice balance for everyone involved.
By the way, in Belgium, you are allowed to film in public places, but not to misuse the image of others if it's disrespecting their private life, unless for legal requirements.