What can I say... I couldn't put it down, and found myself quite liking it after a while. There are some irritatingly heat-over-light sections, such as a general ramble about the arcana that is theoretical physics, but these are wonderfully counter-balanced by the extended geological threads. Most of the stuff on botany was lost on me as I have no grasp of the classifications (genera, phyla, etc.) and he doesn't stop to sketch the tree of life. (Perhaps he did, my (photo)copy was missing ten pages somewhere in the middle.)
I was most disappointed by the sections on DNA and evolution however, coming away with absolutely no new insight into either. Indeed, based on what is said about Charles Darwin I cannot fathom why he was credited with anything.
I could imagine someone coming along and writing something similar but using information as a unifying theme, rather than Planet Earth: one could take the line that local order is increasing (while the universe at large is subject to the second law of thermodynamics, of course) and run with it.
If only science was actually what this book was about. At best Bill Bryson characterises scientific practices ("so-and-so realised that..."), but usually he goes on about the individuals eccentricities rather than the processes (experiments, insights, philosophies) that led to their results. I find it fascinating that Newton and Einstein could have such huge ideas without dirtying their hands with more direct forms of empiricism. (This is somewhat less surprising in computer science as the formal models are more-or-less "cleaned-up" versions of reality.) I fear that modern science is generally a lot more tedious than one might be lead to believe from this book.
There are some good reviews at Amazon. (Having just pasted in some Wikipedia links, I'd have to say you may be better off following your nose there.)