What are the legal conditions for screening public-domain footage in public?

Set up your projector or video screen and run it. Public Domain is just that – public. There are no restrictions on use, so long as you don’t hold it out as your own work.

@ichth nailed it. But, even if it is public domain material, you are still responsible for how you use it. So, if you show something questionable to some kids, you will still take the heat – public domain or not.

There are absolutely no copyright concerns- you could even charge admission, if you wanted to. Take note, however, that there are permits that you may need where you live to set up a public screening.

it depends on wich country you going to do this.
In Italy you must have a permission to use public-domain footage for selling, show anything and so on.