With one exception: the page about the Mercator cylindrical projection. Pater writes that it's “a monstrosity” that “gives us a [colonial] sixteenth century world view”. But Mercator's projection isn't a “monstrosity”, regardless of what you may have heard in that famous (and funny) scene from The West Wing.* This is a persistent myth.
Poor Gerardus Mercator. His projection is perfectly acceptable—if you know why it was designed and what's useful for: sailing and depicting small regions, not the world, as Pater himself mentions; he next wisely proposes the Winkel tripel projection as an alternative for world maps (it's National Geographic's choice.)
We designers must be wary of the possible misuses of the artifacts we create, and do what we can to avoid them. Mercator is indeed often misused; think of Web Mercator, for instance. However, if something is correctly designed—and the Mercator map is—both designers and viewers have a responsibility to pay attention, make an effort to understand it, and use it just for the purposes it's intended for. This is the theme of the last chapter of How Charts Lie.
(Update: M.F. Hartmann points out a possible mistake on the page: I didn't notice it, but that projection doesn't seem to be Mercator's, but the Gall Stereographic projection, which also distorts area, but not as badly.)
* Side note: as Mark Monmonier chronicled in his masterful Rhumb Lines and Map Wars: A Social History of the Mercator Projection, the Gall-Peters projection is sometimes proposed as an alternative to Mercator. I agree with Monmonier when he writes that Arno Peters, one of the creators of that projection, was an effective self-publicist, and that his projection is a true monstrosity, a twisted and ugly one. Instead, choose a compromise projection when designing world maps.
