This was a decent read but not the most exciting book.
The general view Gleeson takes of Law is quite positive. This seems to have been a result of gradually changing opinion of Law in various studies of his life over the time from when he lived to now. As far as I understand it, not having read any other sources except wikipedia, Law was basically seen as a villian, clever but thoroughly dishonest, for some time after his life. Then gradually the biographies and studies began to take a more positive tone. This book hews close to the idea that Law's tragic flaw was that he was an idealist in the sense that he didn't take other peoples weaknesses seriously enough. Gleeson doesn't provide a whole lot of concrete evidence for her view of the man. I realize that this was a popular and not an academic biography but it still seems that if you are going to present a contentious view of a person you should do a little more work arguing your case. Gleeson often will say things to the effect of "He must have felt awful about this...". I understand the urge of the biographer to get inside their subjects head, and I would rather read a positive biography than a negative one, but I felt fairly skeptical in the end.
Another aspect of the biography that was a little weak was just the feeling that you don't get very close to Law himself. He always seemed pretty distant to me while I was reading. To be fair to Gleeson this may have had to do with a dearth of documentary evidence.
On the other hand, despite her generally warm appraisal of Law, she seemed to me to do a decent job presenting the whole mess of the Mississippi bubble in all it's nastiness. One thing that amazed me was the fact that as opposed to the American stock bubble, this French one was forced on the people by the law itself. Law as minister of finance was able to pass laws requiring people to invest in his bank which was the first part of the whole system. Admittedly the stock frenzy was mostly voluntary, but the whole fact of forcing people into the paper currency which became worthless as a result of the fiasco means that it was basically impossible to be smart about it. That is there was no real escape either due to your own wisdom or to luck. Furthermore, in the name of the stock values people were wholesale deported to Louisiana. They actually also passed laws prohibiting people from buying things like gold and silver or other luxury items in order to force them to keep their wealth in the paper currency. All of this has a certain logic from the point of view of propping up the value of the currency but seems quite ruthless given what happened. There are more examples of this sort.
All in all it was a interesting and worthwhile read.