Revealing mistake: When Kevin's cousin Fuller is trapped behind the kitchen chair during the spilled soda incident, the "wooden" chair back which hits him in the nose actually bends when it hits his face. (00:09:25)
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.
Continuity mistake: Marv is walking up steps covered in tar in the basement. He gets some tar on his feet and we see it in the nail scene. When he falls and grabs his feet, his feet are clean from then on.
Suggested correction: His feet are not clean from then on. Although the shot referred to is not clear the next scene shows him leaving the basement barefoot with tar on the soles and sides of his feet. He even leaves black footprints on his way out.
Factual error: Kate flies American Airlines to Scranton, but that airline did not serve Scranton in 1990. Also, a DC-10 is too big to be serviced at Scranton.
Suggested correction: Air Force One, which is quite a bit larger than a DC-10, has landed at Scranton in the past (https://wnep.com/2013/08/22/air-force-one-lands-in-scranton/). Just because DC-10s don't generally land there doesn't mean they can't.
They are much more likely to make an exception for Air Force One than the are for a single family unless it was for something wrong with the flight or an emergency on the flight, not for a connecting flight to Chicago or a chance at a connecting flight.
The idea is that DC-10s can land there for whatever reason.
The news article is from 2013. 23 years after the film. A lot of things can change in 23 years.
Kate landed at Dallas first, then flew to Scranton. This is revealed in Kate's rant at the ticket agent.
Air Force One would park at GA parking, not at the terminal. The DC-10 that lands would have very likely parked at a gate for only 737s and smaller.
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.

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 shot where Buzz is eating the slice of pizza, he is shoving it into his mouth all bent up. In the next shot from another angle, he is eating it flat and it seems to be a whole new slice. (00:08:50)
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: When Kevin is hiding in the nativity set, you can see him on the right, just covered in the green robe. When it changes to the close up shot, he's now holding a shepherd's staff, which would have been visible in the previous shot.
Suggested correction: There is a staff but it's hard to see. If you squint a little, you will see it.
Then you're seeing something else because it would be easy to spot and there's nothing there.
Kevin is definitely holding the staff in all shots, you can see the curved head of the staff against the background.
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.
Visible crew/equipment: When Kevin's sleigh flies through the entrance door, the person riding it is an obvious stunt: Bulkier and way bigger than Kevin.
Visible crew/equipment: When Kevin is getting ready to light the firecrackers you can see a crew member's face reflected on the dishwasher.
Visible crew/equipment: When Marv is in the basement he closes the door behind him while he is getting ready to be hit by the iron you can see a crew member reflected on the basement door.