At no point have I seen anyone point out a factual error that Zinn has made, only that people don't like the conclusions he draws from those facts. Another commonly repeated point is that there are other historical works that do a better job than A People's History. That is almost certainly true as well, but that claim is no more relevant than pointing out that there are better scientific works that do a better job than Einstein's "Relativity: The Special and General Theory".
Having read A People's History, the very beginning of the book explicitly states that he is biased, that bias is something very hard to escape in almost any social study and is present among almost all historical literature whether the author admits it or not, and that the difference between his book and other historical works is that he makes the conscious decision to be biased from the point of view of the people who were conquered as opposed to writing from the point of view of the people who did the conquering.
Certainly Zinn has likely made some errors, but none of them are in the link you provided (as far as I could tell).
Come to think about of it actually, it's also similar with the criticism of David Graeber's (RIP) book "Debt", which usually focus on "well, he wrote something really wrong paragraph about Apple, so you can't believe anything he writes really"
This is not the limit of criticism of history scholarship. Braudel's Civilization and Capitalism isn't considered dated because of factual errors but instead because it over-represents a particular narrative and analysis style that fails to paint a detailed picture of things.
History scholarship is absolutely not a list of facts. It is the construction of a narrative from source material. A text that is 100% truthful to fact can still be entirely bogus scholarship (I'm not saying that Zinn's is).
I happen to disagree with a lot of his political opinions but I think it's very important that APHUS exists.