1) Show a distorted fact attributable to his world view and the objective evidence that it is a distortion.
That's not even hard. Just looking at a recent claim by Zinn concerning the Clinton sex scandal:
"He [Truman] deceived the nation and the world when he described Hiroshima-which he had just devastated by atomic bomb-as 'an important Japanese Army base.' "
Actually what Truman said was:
"The world will note that the first atomic bomb was dropped on Hiroshima, a military base. That was because we wished in this first attack to avoid, insofar as possible, the killing of civilians. But that attack is only a warning of things to come. If Japan does not surrender, bombs will have to be dropped on her war industries and, unfortunately, thousands of civilian lives will be lost. "
(My emphasis in both cases).
Zinn obviously distorts the quote by adding the word "important", "Japanese" and changing "military" to "army". This is because he wants us to think that Truman implied Hiroshima was a "base" in the sense of an "army base" like Ft. Hood -- no civilians -- while the words Truman actually used ("military base") are far more general, and could easily be used for a city that has important military installations.
Zinn "forgets" to mention that Hiroshima was indeed a military base in the sense Truman obviously meant, including tens of thousands of soldiers, important headquarters, massive air defenses, military factories, etc. Simon and Shuster's History of WWII, for example, notes that Hiroshima's normal population was doubled during the war with the addition of military personnel, factories, etc.
What's more, Zinn also "forgets" to note the context of the speech or the rest of the quote, which proves of course that Truman's point was not to deny civilians were killed by saying it was only a civilians-free army base, as Zinn insinuates. Not only does he explicitly admit (and tries to justify) the killing of civilians in such attacks, but anybody looking in the Atlas to see what the hell this "Hiroshima" place was, or looking at newspaper pictures, already knew Hiroshima was also a city.
Where, then, is the "deception" in Truman's claims? Perhaps Truman was wrong and a city being a military base is not good enough of a justification for bombing it. But Truman did not deceive anybody. Everybody listening knew Hiroshima was a city with civilians; it was also a military base, just like Truman said; and he explicitly admits civilians are killed in such attacks.
Zinn is simply lying when he speaks of Truman "deceiving" anybody -- and tries to "prove" this lie by both suggestio falsi (changing Truman's actual words to make it look as if he meant to suggest Hiroshima was only a military base and no civilians were killed) and suppresio veri (cutting out -- oops! Sorry! -- the rest of the quote, ignoring the context of the speech, and the fact that Hiroshima was in fact a military base).
Good enough a misquote, distortion, and insinuation for you?
Now, let's see: how did I get to this lie by Zinn in the first place, you might ask? Let us see: I checked google for "criticism of Howard Zinn" just to see what I shall get, in order to vary my examples a little.
Well, mirablis dictu, the very first link google returns which isn't simply Zinn's or A People's History's wikipedia page is the article by Zinn I linked to above. The article's very first claim about an historical figure (Truman) is a lie -- saying that Truman "deceived" to the American people about Hiroshima -- and is "supported" by Zinn by his usual combination of suggestio falsi and suppresio veri.
Now, what does that tell you about Zinn's credibility?