When Moe throws the 45 record, "It's Raining Men", out the window, it hits Smithers in the head as he's driving by. Afterward, Smithers drives past King Toot's Music and then Moe's Tavern. He would have long passed both places after the incident.
On the plane, they say that economy class is overbooked, so Bart and Lisa can go in first class, but in following scenes, especially when they are focused on Marge panicking, there are several empty seats.
When Marge cooks massive amounts of food, one of the things she's cooked is a cake that she pulls out of the oven fully-frosted. Cakes are not baked with frosting; it is generally applied after the cake has cooled.
When Homer goes to Cheers, Carla tells Sam he can't go out with two twins. There was no reason to mention there were two of them. This may have been intentional, considering the way Carla would often talk on the actual Cheers (1982).
In this episode, Marge shows her fear of flying, yet three seasons earlier in "Mr. Lisa Goes to Washington" Marge is perfectly fine on a plane.