After Marge wakes up, the calendar shows September with 31 days.
Several ex-presidents attend Mr. Burns' birthday party. The bouncer allows Ronald Reagan and Richard Nixon to enter, but refuses to admit George Bush Sr. because he was a one-termer. However, Nixon also served only one term, but he was admitted anyway. Nixon was elected to two terms, although he resigned during his second term, the only President to do so.
When Mr. Burns and Smithers fall off the roof of the kitchen (after Homer has eaten 64 slices of cheese), Marge is heard gasping, but her lips remain in a smile.
The "lights over Australia" would have to be prerecorded as evening in Springfield (regardless of what state its in!) would be daytime in Australia, especially on September 15.
When Mr. Burns and Smithers break into the house and use suction cups to climb through the kitchen ceiling, the door next to the refrigerator opens directly to the garage, which is inconsistent with most episodes that show a hallway leading to the garage.