Bearing in mind that there are plenty of acclaimed books that take a more modern approach, comparison between this book and others would be useful. I am reading some of them. (I can't picture what a post-modern history of the world would consist of. I can imagine a 'deconstruction' of J.M. Roberts, but that is just a fancy word for saying why someone was wrong/biased/too ideological, and it would be confined to a preface or introduction.)
I just ordered a cheaper earlier edition of this book. I decided it is probably worthwhile, even if it may contain more of the author's ideology than more modern books, and compared to the more specialist texts I am used to, I may not like the author's tone. (Roberts wrote these books for a popular audience.) But I don't read much history,variety is the spice of life. Still, it didn't encourage me that some of the people recommending J.M. Roberts seem slightly closed-minded or militant (''Undergraduates, understandably, prefer this approach to the impenetrable jargon of post-modermism''). what encourages me are the two 4 star reviews, and a couple 5 star reviews, on the customer reviews of the 1995 edition.
Whatever Marr's merits or faults, he was writing a shorter book + tv series for a popular audience (or 'an even more popular audience') and he is basing it on modern scholarship, so it was less centred on Europe, although he explains, he chose to favour what he calls an (old fashioned) 'great man and great woman approach'. I'm not sure where you imagine that he demonstrates a 'paucity of knowledge'. There are longer modern books available aimed at the common reader.