Is this currently considered valid?

Not really, no.

"Civilization" was aired in the late 1960s. Our thinking on the development of culture(s) around the world-- and our information on ancient societies worldwide-- has grown by leaps and bounds since the 1960s. Just in terms of how archaeological sites are identified and excavated, and the significant refinement of radiocarbon dating, we know significantly more today about the past than we did when that series aired.

It would be impossible to detail here the number of significant advances that have occurred in practically every field since the series was produced almost 50 years ago. But chief among them (at least, if you want to approach this from the perspective of "civilization") is the information that we now have about the timing of the development of domestication around the world, and the number of times that cultures worldwide independently domesticated animals and / or plants (at last count: SW Asia, Northeastern and Southeastern China, Africa, North America, Central America, South America, and possibly New Guinea).

Not to mention our far better understanding of the climatic history of the Holocene period, which in many cases can be linked circumstantially to the development of domestication, large-scale migration events, and even societal collapses.

A good case could be made that the only mostly universal "leaps" around the world since the beginning of the Holocene are associated with major climate events, e.g., the Younger Dryas, the 8.2 kiloyear event, 5.9 kiloyear event, the 4.2 kiloyear event, the Medieval Warm Period, the Little Ice Age, and so on. (See "Bond events.")

To some extent, the effects of these climate shifts can be seen in nearly every ancient culture that existed at the time they occurred in the parts of the world where they were felt most intensely (not all climate events were felt evenly or equally around the world).

Edit: It's worth noting that even at the time "Civilization" was produced, it was understood that the mostly Western focus was not particularly well-balanced. But today-- even if you only focused on the history of "Western civilization"-- much of what was presented is no longer considered terribly accurate. There've simply been too many advances in not only what information we have, but how it's interpreted in the broader temporal, environmental, historical, and cultural context.

Maybe you could elaborate OP? What does he mean by "a leap forward"? Who, where, how?