What exactly should they look for? There are some threads about this in an other part of the forum and the suggestions posted by other Asgardians about what people should be filtered out range from possible terrorists to economic refugees to people from India and China to people with the wrong moral values (without specifying what would constitute wrong moral values). And although I do agree with you that we should try to keep Asgardia as safe as possible I am (after reading those posts) really afraid of what the consequences might be of creating a system that limits access to Asgardia...

They should check intelligence and mental health at least. It would be nice to know that only smart and healthy terrorists can enter :D