I'll give a broader reaction to the Palin-Biden nothing-burger a bit later on, but the single most mystifying moment in the debate came when she seemed to out-Cheney Dick Cheney in terms of power-grabbing. Palin asserted that a vice president's job is "not only to preside over the Senate" and that "the Constitution would allow a bit more authority given to the vice president if that vice president so chose to exert it in working with the Senate."
That doesn't pass the smell test in this simple way: Does anyone really think that Dick Cheney would leave any sort of authority unused? As a practical matter, go read the Constitution and see if you can find any authority beyond being "president" of the Senate, breaking ties, receiving electoral ballots, and succeeding a deceased president. Presumably she thinks that "president of the senate" has secret superpowers—which would come as news to vice presidents going back to John Adams. Who knew that Sarah Palin was a constitutional scholar?