Stupidity: When a cop goes to Kevin's house after being requested by police, he simply knocks on the door and after a few seconds walks away assuming no ones home. Had he actually bothered to announce himself as a cop, Kevin would have opened the door and he would have been found safe.
Continuity mistake: When the McCallisters leave Chicago, they are flying on a DC-10. The plane that arrives in Paris at the end of the flight is a 757. If they changed planes en route, don't you think that the McAllisters would have noticed that Kevin was missing? He isn't old enough to hold his own passport and his parents would have to be there when he boarded the second flight.