The most silly criticism of Hazlitt (and other Austrian free-market economists) is that they aren't "scientific" and in short "don't use enough math". This is an absurd criticism. Firstly, human beings are not deterministic particles who's behaviour can be predicted by simple equations. Any attempt to reduce human behaviour to some mathematical equation is pure non-sense. We must consider human beings as individual entities who can choose, not fixed constants in mathematical formuli.
Secondly, there is a mathematics that is relevant to Austrians. It is chaos theory and network theory. Chaos theory is currently used to predict the weather. The calculus used by Keynes and other idiots like him is completely useless for describing the behaviour of chaotic systems where individual choice is involved. Hazlitt may not mention Chaos Theory. For that, see Murray N. Rothbard, "Choas Theory: Destroying Mathematics from Within?"; and Gene Callahan, "Why Austrians Should Care About Network Science". Anyone with any sympathy for Keynes and his idiotic followers should note that Keynes put forth a "treatise" before General Theory, which was demolished by Hayek. Hayek then made a strategical mistake in not demolishing General Theory, feeling that the book's idiocy stood for itself. Also note that while Hayek recieved a Nobel Prize for work which was basically an extension of Mises business cycle theory (Mises died the year before Hayek's Nobel), Keynes received no Nobel, showing that even the dimwits awarding that title realized Keynes work was inherently worthless.
The next criticism is related to the first: that Hazlitt doesn't discuss game theory. The reason for this is that game theory is particularly unworthy of discussion. Nash, founder of Game Theory, showed that in any finite game, there's an equilibrium in which no player can improve his or her outcome given the other player's strategies (the Nash Equilibrium). This is problematic in several ways. Firstly, there is absolutely no relation between the playing of games (which are less than net-zero, with one winner and one or more losers) and economics. Secondly, only Game Therorists behave in real situations in the ways in which Game Theory predicts. Thirdly, strategies are not data, but choices. Fourth, it is possible to break out of the specified game to achieve a superior result.
One particularly ignorant reviewer says that in a completely unhampered free market, monopolies form, destroying competition. This is non-sense. Empirically, Ancient Ireland was a completely Stateless society for a thousand years, with a completely unhampered free market, and no-such thing occured. And of course it is a bunch of non-sense that can't happen in reality anyeways. A monopoly is only harmful if you have monopoly prices. But in a completely free market, even if someone obtains 100% of all (say) rail-roads, there is still competition between that form of transportation and other forms, thus monopoly prices cannot be charged. The only time real monopolies with monopoly pricing have emerged is because of State interference.
This may not be the best book on economics that you can read (look to Mises' "Human Action" for what is most likely the strongest treatise on "economics" [actually praxeology, a much larger field]) ever written.