The problem with Garrosh is honestly that he was consistently promoted based more on his father's name and pure dumb luck then anything resembling intelligence or tactical skill.
When we first saw him in BC he was obstinately leader of the Mag'har. I say obstinately because he preferred to mope about feeling sorry for himself rather then actually leading, and as far as I can tell it wasn't all that clear why he became leader of Garadar to begin with. He did pull himself out of his stupor thanks to Thrall, but that was at the tail end of the story arc.
Fast-forward to WotLK, Thrall see's fit to place Garrosh in command of the entire Horde offensive into Northrend, more or less because he was Grom's son. Never mind the fact that Garrosh had never really commanded anything remotely similar in scale, and he had never so much as set foot on Azeroth. Garrosh then proceeds to endorse overly aggressive tactics that would of caused the Horde expedition (and possibly the Alliance's as well) to be demolished had he not been kept in check by better Orcs such as Thrall and Saurfang. He also to lobbed petty insults at almost everyone, be they Horde, Alliance, or neutral for no particular reason at all.
Then in Cataclysm he's appointed Warchief! Why? Because the defeat of the Lich King was somehow falsely attributed to him and the common people wanted him. After attaining power he proceeded to attack the Alliance at every possible opportunity despite the fact there was an evil Dragon flying around trying to make the world explode. Sure he had occasional flashes of lucidity, but he still nearly caused the offensive into the Twilight Highlands to be a bust for both factions.
Now he's basically become so consumed by dreams of conquering the world that his own allies are starting to turn on him. The simple fact is world conquest just isn't what most of the other Horde leaders are interested in. Vol'jin and Thrall have already moved against him and Lor'themar is preparing to do the same very soon. It probably won't be long before the other Horde leaders start questioning their Warchief and wondering if there isn't a better way.