From an academic point of view, this book is undoubtedly outdated. Written in the late nineteenth century, there have certainly been advances in our knowledge concerning the areas this book covers (to take one example, the Bogomil identity of the Bosnian Church has been challenged). However this book is still valuable since few if any historians have attempted such a vast subject, covering the genesis of Muslim communities throughout the world- ranging from Siberia to Cape Town. Arnold's basic thesis that large scale conversions to Islam were not the result of force is still valid, borne out by modern scholars such as Hugh Kennedy and Richard Bulliet. His chapters on the Middle East, Christian Africa, Persia and Spain are the most coherent and thorough- given that the conversion of these areas was a single historical process. He mainly attributes the success of Islam to the decadence and the corruption of the local Orthodox churches. Arnold notes the scarcity of accounts of recorded Muslim attempts to convert people, which is a disappointing gap. Despite sporadic persecutions that occurred, Arnold martials enough contemporary accounts to demonstrate that conversion was generally a matter of choice, even if there were non-spiritual motives involved.
His chapters on Africa, India, Central Asia, and China are also interesting, even if necessarily less thorough (every state of India or Africa has its own Muslim story). The chapter on the Malay archipelago (Indonesia), is not as rich in detail- for whatever reason, Arnold provides us with a detailed account of the politics that led to the Muslim state of Demak taking over the Hindu empire of Majapahit, but excludes details of the missionary work of the famous 9 walis, which is far more relevant to Arnold's subject matter. His chapter on Central Asia begins with the Mongols (skipping the earlier Turks as their conversion is probably far more shrouded) and then jumps rather abruptly to the conversions of the indigenous peoples of the Volga in the 19th century (although most of these people are today Russian Orthodox).
Besides the history, the most interesting parts of Arnold's book are the aspects of social history regarding the spread of Islam- including the autobiographical account of a Hindu Brahmin who converted to Islam, memoirs of a Spanish Muslim refugee from Granada bemoaning the fate of the tolerant Spanish Muslim kingdom, two letters from Central Asian potentates inviting the emperor of China to embrace Islam, reflections of African slaves who embraced Islam while in captivity, the accounts of an Egyptian Jew transfixed at the sight of a Friday prayer, and the accounts of European prisoners in the Ottoman world. It is accounts such as this which fill in the bare bones of Muslim history and provide a vivid glance at what the Muslim faith has meant to its followers, particularly converts, over the centuries.
It helps to read this in conjunction with wikipedia, as Arnold often uses older names, such as Galla (now Oromi), Cheremiss (now Votiak), etc.