This is almost certainly the definite description of the background and history of the atomic bomb, from the beginning of the discovery of the atom starting around 1900 to the detonations of the two bombs over Hiroshima and Nagasaki in 1945. Richard Rhodes gives very good descriptions of the basic facts of the physics and engineering, and also provides an overall comprehensible explanation of the politics of the process. Having some previous knowledge of the basic theory and history of nuclear physics, I cannot find any mistakes or misleading statements of any consequence. As a Swede, I notice that the southern port of Limhamn is misspelled Linhamm.
One important point the author makes is that the realization that the atomic bomb would be a theoretical possibility was inevitable, given any scientific investigation into nuclear physics and chemistry. At no point was there a possibility of containing the knowledge to a select few. However, it is also clear that the actual making of a bomb required a huge engineering effort, which in the end only USA could muster during the Second World War.
Another important point is that the advances in nuclear physics were very much a collective affair. No single discovery by any single scientists was the turning point. Multiple discoveries and ideas had to be made for this to progress.
Somewhat appropriately, I finished this book on July 16th, on the anniversary of the Trinity test, the first detonation of a nuclear device ever. The final chapter of the book documents the terrible consequences of the detonation over Hiroshima in the form of a series of quotes from the testimony of surviving victims. It is excruciating reading.