Well, for one - the removal of certain ministers (or 'dissolution' of the government - that is to force a new election in the event that the government is paralised by a lack of a majority) at the legislative/representative branch's approval; or the appointment of certain government officials in the case that no one wants or fills that position.
I'd have to check the 'Nuk and Aussie constitutions for the exact details of who this is accomplished. It's been a while since I resided in Soviet Canuckistan or Oz, but their particular varieties of the Westminster Parliamentary System does make for quick turnovers of political power and forces government to be active.
As a proud Canadian, the powers of the GG ( the representative of the Queen, the true sole executive power) is only ceremonial. No laws can pass without "royal assent" which is the signature of the Governor General. While the GG has the power to stop any law and government from coming to fruition, to do this would be against customs and convention and cause massive uproar from the populace.
Also the existing Prime Minister gives the name of who s/he wishes to be Governor General which the Queen of England then appoints, true the Queen can appoint whoever she wants but that is once again, against customs and convention. The GG also dissolutes governments at the advice of the Prime Minister, there has only been one situation of where the GG did so without the permission of the Prime Minister and it's known as the King-Byng affair which lead to a major international tiff and major anti-british sentiment.
The powers of the Governor General and the Queen are over-stated to represent our traditions of being ruled by England, and they are in name only.
The executive named in the constitution is the Queen/GG but in reality, is the Prime Minister and Cabinet. In the constitution, the PM and Cabinet are supposed to be fused with the legislative (why they run as candidates in ridings and why you vote for the party and not the executive) but once again in reality it is quite different.
As for the Soviet Canukistan comment, low blow! Also, what? You haven't heard, we've got a raging Conservative PM ready to bow to the American foreign policy at anytime no matter how misguided, dismantle public healthcare for American Insurance companies, surrender Canadian territory AND make additional grand trade concessions for (un) free trade!