The act of videotaping someone with or without permission in public or private spaces is not illegal. Just imagine all those security cameras. However, if you aim a video camera up someone's skirt, whether in public or private, that is voyeurism. You had better have permission for that. In fact, it is voyeurism even if you do it without a camera. Same logic applies to hidden cameras inside apartment units (or even bathrooms).
If you are inside a shopping mall, grocery store, any retail outlet or someone else's home, you will have to go by their rules on what they allow you to videotape.
As for broadcasting, anything that is newsworthy may be shown without permissions.
