It's a brave and interesting strategy, but it does have its drawbacks. Any history of the last century is going to run into the basic difficulty that "the last century" is a rather arbitrary category - do we, at the end of the century, have that much in common with our ancestors in 1900? What happened in 1901 to make it so different from 1899? Tusa nudged that point himself, talking about scientific and technical progress: "In 1901, Nobel prizes were awarded for the discovery of X-rays and the diphtheria anti-toxin; adrenalin was discovered, too; Marconi received the first transatlantic phone message; instant coffee was invented, so was the first vacuum cleaner, and the first shop selling safety razors was opened. Where's the meaning in all that?" Well, where do you want it to be? History isn't meaningful, except when we impose meanings on it.
Because the 20th century is such a nebulous entity, Tusa occasionally ends up talking about it in a nebulous rhetoric that seems out of character - he has a particular weakness for pairs of contraries of the "best of times, worst of times" school ("This was the century that dreamed the impossible and invented the everyday, the century that searched for knowledge but struggled for understanding, that longed for love but found relationships", etc). It doesn't help that such a volume of ideas is packed in - on science, the arts, Marx, Freud, Gandhi, American individualism; necessarily, some or most of them get skimped on. At one point, for example, Tusa talked about music being obsessed with mathematical rules as opposed to classical ideas of harmony and melody; well, that's true of a very small number of composers in a small geographical area over a short period of time, but it doesn't say anything about most people's experience of music.
Tusa himself made a remark at one point about 20/ 20 being a series of sketches which, when you see them all together, will give some idea of the big picture; and perhaps that's one reason for the sense of disjointedness - he's not actually trying to present a coherent package the first time out. In 19 programmes time, it may all be looking very different. For the moment, though, it leaves you with a mild case of the 20th-century blues.