Enough of this! 
Hawke did not mess up. She killed that thing. She checked its body. Varric checked the body. Bethany and Fenris, too. It was dead. How is that messing up?
If one cheats at Poker how is it the fault of the other players?
What could she have done? Stab and burn the body and spill acid over it and bury it and stab it again? Even that would not have helped a bit because the soul had not cared and simply hopped on. Corypheus had not yet split his life force into separate parts and planted one part in a corrupted dragon, so there was basically no way of really killing him at that time (stupid plan of his doing that, thinking about it now).
There is no way to compare her believing a cold dead body implied a cold dead soul to Solas' deliberate act of throwing the ball and risking an interception instead of giving it to Lynch and letting him break through the defense carrying it giving the orb to Corypheus willingly, vaguely hoping to kill him in the process of using it (if that is true).
I don't like to constantly hear how Hawke is a single big mistake. That's not funny! I spent multiple playthroughs with her, Kirkwall felt like home, I genuinely like her and bonded so much stronger with her than any of the rather characterless characters. Hawke was awsome. 
I'm not actually annoyed. But Hawke also did not actually mess up anything.

As a Washingtonian, I feel like I should be vaguely outraged.
As myself, I'm vaguely impressed I even caught the Superbowl reference. 
But yeah. Hawke's main screw-up was not being the Ultimate Hero That Has the Power of Plot to Fix Everything. She wasn't perfect, but she was much better than most.
The red lyrium was Bartrand's fault, largely. And Hawke and Varric's mistake there was one of ignorance and innocence.
While I would have been suspicious of Larius in Hawke's situation, namely the grammar change to fit Cory's, I doubt I would have tackled him. Even then, it would have solved nothing. Once Corypheus was out, he was out.
Makes you wonder how they got him sealed up in the first place.
As for Act II, the fanatics in the city poked the Arishok with a stick for years, and Hawke (in most playthroughs) is one of the only reasons it didn't happen sooner, and shuts it down fast.
In Act III, the fault is mainly with Anders and Meredith. Meredith, for being completely illogical and homicidal and on red lyrium, and Anders, for deliberately provoking her to make a point to mages across Thedas. (I thought it was dumb at first that blowing up the Chantry would 'solve everything'. But Anders' plan worked pretty much as he wanted it to.)