Continuity mistake: The Murphy's basement is shown to be dripping water from when Marv flooded the kitchen earlier but when the crooks are hit by the old man at the end of the film, the floor is dry even though the faucets are still running.
Continuity mistake: As Marv loses his last sock on the tarred stairs, his heel does not make contact with the tar. Later, when he picks up the crowbar to walk out, his whole foot is now covered in tar.
Continuity mistake: The amount of tar on Marv's feet changes from all over the bottom and sides, to just the bottom to almost none. Even though he walked through the snow, the tar would not just wash off.
Revealing mistake: When Harry tells Marv that he's sick of him leaving the water running in the house that they robbed, you can see Harry supposedly shift his van into drive. However, Harry does not even move the gear selector from park to drive.
Revealing mistake: Kevin goes food shopping, He gets milk and detergent, obviously heavy items. Afterwards we see him walking home and the bags he is carrying break open. He is carrying them like they are light as a feather. Even when the milk falls, you can tell it's an empty bottle.
Factual error: When Kevin's mom stays behind at the Paris Airport to wait for a flight home, she is shown in a gate area in front of a huge picture window. Outside can be seen an aircraft, a 727 in Eastern Airlines livery, in what is actually Chicago's O'Hare Airport. Eastern never flew to Paris and the aircraft would not have the range for such a flight. Also, you can see a sign that lists Terminal E and F, which are at ORD. They do not have these at Paris ORY.
Continuity mistake: In the scene where Kevin goes flying into his treehouse and breaks out the wood, the amount of wood missing changes from one scene to the next.
Continuity mistake: When Kevin is preening himself in the mirror while giving a running commentary of his washing habits, you can see the shower gel (facing forward), aftershave and deodorant to his left by the sink. When it cuts to a close shot, a bottle of fragrance has mysteriously appeared by these items and the shower gel is facing away from Kevin.
Continuity mistake: In the scene where Harry tells Marv to go down to the basement door, Marv slips on the icy stairs and falls down to the bottom of the stairwell. At the bottom of the stairs from the camera shot from above you can see an accumulation of snow on the stairs and in the bottom stair well. Yet when Marv finally opens the door and enters the basement all the snow that had accumulated in the stair well has now disappeared.
Continuity mistake: When Kevin's mom is in Scranton at the airport counter, her coat is resting on her shoulders so that it's open. In the next shot, the coat is closed more, so the sides are close together.
Revealing mistake: When Harry and Marv are crossing the "rope" to the treehouse in the far away shots it is something thinner and resembling more like a steel cable, not a rope as Kevin had put up.
Character mistake: When the family comes home, Kevin says he went shopping and bought milk, eggs, and fabric softener. We never seen him unload the eggs onto the conveyer belt at the store nor did we see the check-out lady scan them.
Factual error: Assuming the McCallisters left Chicago mid-morning as the story suggests (say, between 9 and 10am), and allowing for an 8 hour flight and 7 hour time difference, the flight should be arriving in Paris somewhere between midnight and 1am. However, the footage of the plane landing suggests it is around twilight.
Continuity mistake: In the scene where the robber is breaking into the basement, the steps and concrete by the door are icy. However, when the camera angle changes and it shows the same scene looking out of the basement, there is no ice at all.
Visible crew/equipment: When Kevin is going to swing over by the tree house on a rope, before he goes you can see a crew member reflected on the wall by the window.
Continuity mistake: When Harry is telling Marv when the Christmas lights on the house are going off, right before they are going to rob the house, they show the dashboard of the van. There is nothing on it. When they pull into the driveway, there's paper and other things on the dashboard.
Continuity mistake: When Harry and Marv are first stalking Kevin in their van, they pull up to the curb and stop at an angle to it. In the next shot, the view out the back of the van and the view of the van from the front show the van parked parallel to the curb.
Continuity mistake: As Kevin runs away from the nativity scene after hiding from the Harry and Marv, his scarf is done up to the right (over his right shoulder). When he reveals himself from the nativity scene from under the green robe, his scarf is done up to the left (over his left shoulder).
Continuity mistake: The iron that hits Marvin strikes his forehead, but after, the imprint is across his whole face.
Continuity mistake: When the robber with the beard gets hit in the face with an iron, the iron hits him on the face, and leaves a mark slanted to the right. It also leaves a mark on his nose. When the two robbers are talking after they have been tricked and before Kevin puts the spider on one of the robbers, the iron mark is vertical and there is no mark on the nose anymore.
Answer: I think it was a way to make leaving him "home alone" more realistic and understandable as opposed to absurd. Being perceived as a brat/pest and annoying to be around, it is (somewhat) conceivable that none of the family members would be eager to have Kevin by their side. This "frees" all of them from noticing that Kevin isn't with them. Everyone would just assume that Kevin is somewhere among them and each be glad they didn't have to sit next to him on the way to the airport or during the long flight.
KeyZOid
In addition to this, the movie is partially about Kevin learning to have more respect for others. He appreciates his family more as he spends more time without them.