Determining whether or not a minority government is dissolved, and an election is held, or if a ruling coalition can be allowed to form.
In 2008, right after the election the GG did the ruling minority of Tories a pretty big favor by refusing to accept a non-confidence vote by a majority coalition, and instead, proroguing parliament for the benefit of the ruling minority party...
Absolutely insane. (That this question is left to the whim of one unelected person.)