These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: The Chaser's War On Everything
Crosses the Line Twice: Pretty much the whole point, although the APEC incident and the Eulogy Song are most famous.
Not to mention the Make A Realistic Wish Foundation.
Crowning Moment Of Awesome: Driving a blatantly fake motorcade brazenly into the most high-security area in Australia during the APEC summit, pulling up outside the hotel where George Bush was staying and having Chas get out of the car dressed as Osama Bin Laden!
And then they arrested the other guy!
The guys that weren't part of the motorcade (and so, weren't in jail) approached the same area the next day in "Play School cars" (cardboard boxes with paper dinner plates for wheels), claiming to be a motorcade and asking to be let through please. You know, just to rub it in their faces.
For the Oscar Bait sketch, it did get at least one complaint about its portrayal of Andrew's disability (an obvious reference to My Left Foot), by people missing the point. As for the indefensible Josef Fritzl "Inbredy Bunch" sketch, this troper can only guess that everyone who would have complained had switched off at the end of the "Make a Realistic Wish" sketch, immediately before.
Ear Worm: A number of their song parodies and the show's theme music.
John Lennon chose the hippy life, he chose some nutbag for a wife and his songs were never quite as good as Paul's.