The segment involving Adolf Hitler refers to a conspiracy theory that he survived World War II and escaped to Argentina. Had Hitler indeed survived, he would have been 105 years of age at the time the episode aired.
During the slide show presentation, a slide with plan "B" depicting Fidel Castro in cross hairs is seen (which the government official promptly eats). This was a reference to a conspiracy theory that the U.S. Government, after the failure of the Bay of Pigs Invasion, attempted to have Fidel Castro assassinated.
"That's not a knife: This is a knife!" is a famous line from the film Crocodile Dundee, said by the title character after a robber uses a pocket knife to try and rob him; Dundee pulls out a Bowie knife as he says the quote, intimidating the robber himself. Dundee also appeared in one of Evan Conover's slide pictures.
Earlier Bruno asks his son if there is anything wrong with the bidet, which is another reference to this movie.
The "South O' The Equator Gift Shoppe" is a reference to the tourist attraction "South of the Border", located near the North Carolina/South Carolina border. Their mascot Pedro and his love for bad puns are on display here as well.
During the chase scene from the Australian Parliament, a Mad Max motorcycle gang member can be seen in the crowd.
The booting punishment is a reference to the 1994 caning of American teenager Michael Fay, who was caned several times by Singaporean authorities for vandalizing cars.
The beer brand that the Australian adults are frequently seen drinking is Foster's (which is, in real life, an Australian brand), except with a kangaroo instead of the "F" on its logo.
The bullfrogs destroying the Australian's crops is a possible reference to rabbits and cane toads which were introduced to Australia and destroyed many of Australia's plants.
Despite Homer being very much against the Australians' proposed "booting" punishment, Homer was previously amused when a very similar looking boot struck Bart in the butt in "Burns' Heir".
It would later be revealed in "The Color Yellow" that the Simpsons' ancestors were exiled from Australia.
In this episode's French version, Tobias the Australian Boy is named Toby by his father, Bruno.
In this episode, the Australian's way of economy-- the "Prime Minister" and barn (partially)-- and speaking are stereotypes from other countries. In fact, pretty much everything in this episode is an Australian stereotype.
The Australian Parliament House was previously intended for Austria; the entrance reads "Parliament-haus der Austria." Australians added an "al" and a caret (^) with red paint.
When this episode originally aired, many Australians criticized the episode as a mockery of their country (Mike Reiss even claiming the show was condemned in the country's parliament). However, Australian reception of the episode has improved in recent years, with many Australia-based Simpsons fan pages on social network (containing many references to this episode) and even a petition to rename the Australian currency the "dollarydoo".
While The Simpsons is prone to some errors simply for comic effect, in this particular episode, the supposed scientific knowledge of drains flowing differently in the Southern Hemisphere is actually a myth. The Coriolis effect is indeed accurate, but it is only seen in large systems such as eddies, whirlpools in the ocean, and cyclonic storms such as hurricanes and tornadoes. For small-scale cases such as drains and toilets, there are too many other more-important factors for the effect to make a difference (spin imparted by water's flow, angle, friction, etc.).
Lisa demonstrates "counterclockwise" by making a clockwise circle with her finger.
Bart called for Burkina Faso during his search for answers about the toilet spinning clockwise in the Southern Hemisphere. Burkina Faso is in the Northern Hemisphere. Obviously, Bart doesn't know this. It could be also possible that he called there off-screen but not about his theory of the toilet water spinning but while making a prank call or that another person was calling there but it had nothing to do with the toilet spinning.
Homer didn't particularly oppose booting in "Burns' Heir". Of course even Homer may differentiate between a comedic-style booting and as a punishment for a seemingly small offense, especially when it was never discussed prior.