The World At War is, within the limitations upon it, remarkably accurate. In fact, its biggest weakness cannot be considered its fault; when it was made much important information was still considered 'top secret' or classified... or kept behind the Iron Curtain. Just as an example, there's nothing about the British codebreakers anywhere in the series.

On the other hand, being made in the late '60s/early '70s, many important figures were alive and able to be interviewed for the series. From my own field of "expertise", for example, Minoru Genda and Mitsuo Fuchida, one of the planners of the Pearl Harbor attack and the leader of the first wave of planes respectively, both appear and speak about the events in the Pacific.

For its time and given the limitations of a TV documentary, it's truly brilliant. Even now there's nothing that can stand with it taken as a whole. Individual events (i.e. Stalingrad, Midway) may now have better tv shows available, but that's only because as time has gone on, more information has surfaced about those events.

Is it perfect? No, of course not... it spends more time on Europe and England than the Pacific, for example, but that's understandable considering it was made by Thames Television, a distinctly British production/network/franchise holder/thing. But it's plenty darn good.