I always thought his main fault was his anti-fascism. He always wrote as if he thought the left in the Spanish Civil War, and by implication, the Allies in WW II, were better than their opponents. But I just came across an article by him rejecting the modern anti-fascist diversion in Europe (France, to be precise):

http://www.theweek.co.uk/us/46625/who-are-real-fascists-marine-le-pen-or-united-states

Cockburn, the editor of Counterpunch, rejected

• the "satanic child abuse" panic
• the assumption that the Israel Lobby is subservient to US imperialism
• global warming
• hysteria about "fascists"
• the 9/11 truth movement