Disclaimer: I love Bill Bryson's travel books, finding them to be a much more humorous and sunny alternative to the dour and cynical travel books of people like Paul Theroux. However, I find some of his "histories" to be problemmatic.
"A Short History" is one of his better non-travel books, although it really is a Cliff's Notes guide to the history of major developments in the fields of astronomy, physics, biology and geology.
My main problem with it is that it tells the story of scientific developments without actually providing real insights or understanding of the science it's documenting. Bryson will be the first to admit this, brushing away an much-needed explanation of a difficult concept with a "we don't have time or knowledge to explain it here." It's always easy to tell that Bryson's research is based on secondary sources, which he doesn't footnote. Some of his scenes are little more than rewritten versions of content in other books I've read.
Still, as a one-volume, breezy overview of the history of science it's quite good, although one would be better off reading single volume histories of a particular field written by experts in their field. (I don't have the Bryson in front of me, but I think he has a good bibliography here)
In any case, the book is a hell of a lot better than his absolutely terrible "biography" of Shakespeare.
J-I-B