No one even flinches at the fact there's a strange cop just hanging around the vestibule?

lol. The door bell rang, one of the kids answered the door and let the police officer in, but either neglected to tell the parents properly, or the parents just took their sweet time. As you can see early on in the movie everyone is rushing around getting ready for the trip to Paris.

You see that’s the thing — you’re not the McCallisters. :D

That is the whole joke. This large, loud and rather wild family is so distracted and concerned with whatever they’re doing that they *can’t* notice a random “cop” standing in their home. Even Harry himself is noticeably taken aback by the way everyone is acting and how none of them are paying attention to him. It’s just who this family is. This movie probably wouldn’t have happened if it wasn’t for the “untidy” McCallisters.