Continuity mistake: When Kevin goes to the grocery, he buys Tide detergent. While walking home, the two bags break, but no Tide detergent falls out.
Revealing mistake: As Kevin is flying off the front porch on the toboggan, you can see the small wheels mounted on the bottom of the sled to aid in its "jump". (00:25:30)
Other mistake: Kevin rides down the stairs on his sled and out the door. He originally lined up the sled at the top of the stairs, but it is clear that the stairs lie to the right of the door. His sled went straight down the stairs, therefore making it impossible to go straight out the door in one movement as shown. (00:25:25)

Continuity mistake: When Kevin goes outside the first time and sees the cars in the garage, the light isn't on. When it shows the garage again in the next shot, the light is on. (00:20:25)
Suggested correction: The light could be motion activated. Either Kevin's movement or passing vehicles could have turned it on, regardless of the time of day. I have motion detector lights in my carport and they constantly go on and off in the daytime if it's low-light and cars pass by fast enough. People walking their dogs can also activate it if they are close enough. They sometimes stay on until I have to manually turn the power off, then on again.
That would explain it only if the light came on when Kevin "activated" it. It stays off during the first scene, and he doesn't make any motion towards the garage when the camera is on him. Nor do we see any vehicles or people pass behind him.
How likely is it that this movie - taken in 1990 - had access to the developed technology that we have today, to make automatic lights turn on?
Infrared motion sensors were around in the 80s.
Continuity mistake: When Marley enters the store, his right boot swaps from soaking wet to dry between shots.
Revealing mistake: When Harry trips on the fan string throwing feathers all over him, the fan sound is heard running but there's no air blowing at him as the feathers are falling around him undisturbed. A few shots later, we see the fan on and blowing feathers around the room which is what it should have been doing.
Factual error: When Kevin's mom leaves Paris to return home, the plane shown departing the airport is a DC-9. No airline uses this plane for trans-Atlantic service - it doesn't have the required range.
Suggested correction: Although not explicitly mentioned, it could be a connecting flight which departs Europe from another airport. In this case, flying a short or medium range aircraft to reach a hub airport like Heathrow would be plausible.
They stopped at an intermediate airport to catch a connecting flight and still nobody noticed Kevin was missing? Absolute rubbish. The posting is absolutely correct.

Continuity mistake: When Kevin is leaving the church after talking to the old man that lives next door to him, he runs home. Between leaving the church and getting home he is wearing one pair of trousers, when he gets home he is wearing a pair of jeans, then when he is setting up the traps for the bad guys he is back to the first pair.

Continuity mistake: In the scene where Kevin prepares to ride his toboggan down the stairs, the front door changes position between shots from half open to completely open. (00:25:20)
Revealing mistake: Whenever Marv is outside walking in the snow in his bare feet you can tell that the feet aren't real.
Revealing mistake: The morning the McCallisters are rushing to get to the airport, the kid from across the street is bothering one of the van drivers. In the scene where the van driver says, "Gee, kid I dunno, hit the road," you can clearly see the kid mouthing the words as the man speaks. (00:14:00)

Continuity mistake: When Joe Pesci places his hand on the red hot doorknob on the front door of Kevin's house, he places his hand on the doorknob sideways, but after he sticks his hand in the snow, he looks at his hand and the letter M that was burned into his hand is straight up and down, not sideways like it should be based on how he grabbed the doorknob.

Continuity mistake: In the scene where Kevin is shooting the BB gun at action figures he has lined up along the laundry chute the baseball player figure he sets up is leaning against the left hand side of the laundry chute frame, yet when he begins to shoot at the figures the baseball player is standing up straight on its own and not leaning against the chute frame any longer.

Continuity mistake: When Kevin is putting washing in and taking clothes out of the dryer, he places the orange bottle of liquid on top of the washer with the handle facing away. On taking the clothes out of the drier and closing the door, he turns to see the metal heater scaring him by saying "Kevin." Look over his left shoulder when the shot comes back to Kevin, the orange bottle now has it's handle facing outwards, and the top isn't on properly.
Continuity mistake: Kevin goes out to cut the top off a tree to use as a Christmas tree. The tree top he drags in is much smaller than the one he decorates.
Visible crew/equipment: When Kevin first realises he's home alone and goes into Buzz's room, there is the leg of a crew member to the bottom right of the picture (wearing jeans). (00:19:20)

Continuity mistake: Kevin sits down with a meal before the Wet Bandits arrive at the house consisting of macaroni and cheese on a plate. When Harry eventually makes it to the dining room, he is pelted with feathers. Look at the table to the left. A three part microwave meal still in its white plastic container now sits on the plate.
Revealing mistake: When Kevin rides the rig on the rope to get to the treehouse, you can see that it was a stuntman who is much taller than Kevin and looks nothing like him.
Continuity mistake: When Kevin plays the video when the guy comes to deliver the pizza, the guy on the video says "Hey. I'm gonna give you to the count of ten." When Kevin first saw the movie, the word "Hey" was never spoken. The line immediately before "I'm gonna give you to the count of ten" was "I'll tell you what I'm gonna give you, Snakes".

Character mistake: When Kevin is shooting the toys off the laundry chute with Buzz's BB gun, he's looking through the scope with his closed eye.