J.M. Roberts is a good popular historian. Of the several works of his for the popular audience that I have read, all have come across as interesting and well organised, accessible and fairly objective. Roberts also writes for scholarly audiences; while his popular works are not a rigourous, his other works prove that there is serious scholarship underpinning these works.
Roberts' large, one-volume 'History of the World' joins many such volumes in having strengths and weaknesses, the primary weakness affecting them all being the inherent problem of selectivity. The history of the world, even if one simply means by this the history of human civilisation, has so much data in so many directions that ultimately no single volume (or, indeed, whole series of volumes) will satisfy all on every count.
Roberts begins with the pre-historical beginnings of human beings in various parts of the world, based on archaeological evidence. He then explores of civilisation in various parts of the world (Mesopotamia, Egypt, China, India - all the places civilisation arose largely independently of each other). From there, Roberts traces the advances of civilisation through the Classical Mediterranean period, the post-Roman imperial time, the period of European expansion around the world, the period of world wars, and the modern post-war period. Within these broad divisions, Roberts introduces the history of other parts of the world -- the Islamic civilisation, more advanced the post-Roman lands, is not seen as a mere afterthought or addendum to the 'real' action in Europe; Roberts also traces historical development in China, India, and Japan as major centres of civilisation.
The majority of the text does centre upon the European stage and their expansion around the world, as this historical strand (for better or worse) is still the dominant influence around the world today. More than half the text deals with the past 300-400 years, in which European hegemony politically, militarily, and culturally took hold. Roberts keeps speculation and judgement to a minimum for the most part, reporting the facts of European growth and the response in the various lands around the world.
In my opinion, the primary piece lacking here are New World (western hemisphere) civilisations prior to the colonial conquests. While it is true that the influence of Native American cultures does not have tremendous impact upon the world stage today, it is also true that the civilisations of the Incans, Aztecs, Mayans and others were at least as interesting and advanced as various Sumerian and Egyptian ancient civilisations, even if they lack the historical continuity to today's world.
Roberts does add the occasional 'colour commentary' to his analysis. For example, in discussing the Lutheran Reformation, he mentions that Luther replaced the idea of eucharistic transubstantiation (the idea that the bread and wine become the body and blood of Christ) 'with a view which is even more difficult to grasp'. Roberts' biases are definitely Eurocentric and toward a progressive, humanist view of history's path. However, there can be no total objectivity in any historical presentation, and Roberts keeps his biases in check for the most part.
There are nearly 100 maps, and hundreds of images and graphics, including many full-colour plates. These are photographs of places, artifacts, paintings, and other images of importance serving to highlight the text. There is a worthwhile index. The text lacks recommendations for further readings, which is a drawback, given the survey nature of the text. However, it is one of the better single-volume histories of the world available today, particularly for those who are looking for broad historical trends leading to the present day.