Anyone take a step back, and realize Garrosh is doing what just about any Warsong Orc would be doing? Loud? Check! Obnoxious? Check! Craving the blood of the enemy? CHECK!
Thrall put Garrosh in charge, because he is an Orc of the old ways! Look at his skin, and you can see this! In addition he is a veteran of the Northrend campaign, and having the guy who was apart of defeating the Lich King, is what Thrall viewed as being good for his people, since he was busy delving into his shamanistic ways. Why not Saurfang? Well he was busy mourning the death of his son. I digress...
Garrosh is a Warsong Orc at heart, and when he looked to his father's history he at first viewed it as a disgrace, but was then told of Grom's heroic ending and suddenly viewed the previous traits listed above as being admiral! Gaining this sudden sense of pride, he displayed this in Northrend, and that lead to him to eventually gain the trust of the Horde (Note: The majority of these people being Orcs) to become their Warchief. This is where things go downhill for the Horde...
Thrall made the mistake of giving to much power to the immature Hellscream. Garrosh is a deadly soldier ready to unleash on the Alliance, but when it comes to the whole position of Warchief that is a different story. When taunted by Garrosh in the events leading to Northrend, Thrall should have simply dusted it off, the way an adult does to a insult from a child.
In the current state of things, I do not view Garrosh as doing wrong, I simply see with each error he preforms this being Thrall's mistake for giving the young Orc so much power over the people. What would have been best for Garrosh is to have him train under Saurfang, and turn the young Hellscream into a killing machine who could uphold honor.
I am personally sad to see the last heir to the Hellscream (as far as we know) throne be tainted as he currently is. Not by the demons in RFC, not by the Sha in Pandaria, but by Thrall for making a bad call, and expecting Garrosh to be civilized as Thrall is.
So the question here is who is to blame? Thrall for giving the power to Garrosh? Garrosh for taking the mantel of Warchief? Or another possible source/outcome theorized within the community?