When Homer and Bush are fighting in the street, just before Bush realizes Mikhail Gorbachev is there, Bush's car and the damage he did to the Simpsons' front yard disappears and re-appears.
Bush's place is seen to have a high black-bared fence and tall green hedges around it, yet when Homer launches bottle rockets at the house, there is no bared-fence or hedges.
The Flanders call to say hello to George Bush, Barbara brings out 5 glasses and a jug of lemonade. Immediately (no time for Bar to go back in) we see all four of the Flandereses and both Bushes drinking.
Barbara Bush met the Simpsons in "Mr. Lisa Goes to Washington" but seems to have forgotten that fact here.
Grampa claims he was "spanked by Grover Cleveland in two non-consecutive occasions." This is obviously a joke based on the fact that Cleveland was the only president to serve two non-consecutive terms as president, but it is highly unlikely that this is true, as Cleveland died in 1908, and later in the series, Grampa is revealed to have been a young boy during World War I, and thereby likely not alive at the same time as Cleveland.
Apu sings the lyrics to Cheap Trick's "Dream Police" incorrectly.