Look at the first example, "The Broken Window." The author describes a situation in which:
• Some kid breaks a baker's window.
• The crowd that gathers notes that, although unfortunate for the baker, the broken window will provide work for a glazier.
• The crowd fails to realize that the baker was planning to buy a suit, and the work provided for the glazier is counterbalanced by the work lost by the tailor. Also the baker's out a suit.
That's all well and good, but the author never considers the scenario where the baker is wealthy and losing $250 will not affect his spending habits (over at least the course of decades). Then the broken window actually results in $250 of created work for the glazier without any corresponding loss of work elsewhere (by e.g. the tailor) or loss of value (by e.g. the baker, who in the book's scenario couldn't buy a suit because of the broken window). In this scenario, the broken window is actually a net win for the community.
Nor does he consider the scenario where the baker is poor but thrifty and tends to save what he has. This is a very complex situation: in the short run the thrifty baker's spending habits will probably be unchanged by having to replace a window (or at least negligibly changed relative to the $250 that he was forced to spend), but in the long run he probably will end up spending about $250 less because of what he shelled out to the glazier, and moreover will fail to procure some items of value about $250. So then the math goes like this: because of the broken window, the glazier gains $250 dollars of work today. But some other worker loses $250 of work down the line, and the baker, in the long run, loses some items of value $250.
The thing is, spending $250 today creates more work than spending $250 next year, because the money will keep circulating, so it's not easy to demonstrate that the broken window is either helpful or harmful to the community here. (Note: spending $250 today instead of next year has a host of other effects, like increased inflation, that I obviously didn't mention. I don't mean to make a full analysis of these scenarios, just to point out that the author didn't make a full analysis of them himself.)
And a more glaring failure of logic in the second applied lesson: the author says, "No man would want to have his own property destroyed either in war or in peace. What is harmful or disastrous to an individual must be equally harmful or disastrous to the collection of individuals that make up a nation."
That's just not true. (A slightly ridiculous counterexample: when a serial killer dies of a heart attack, the nation he lives in is probably bettered.)
(In spite of all this, I still kind of liked the book.)