He could do with considering more animals beyond primates. The talk doesn't go very far beyond examining how humans are different from chimps, and he's probably unconsciously set up a hierarchy there, with humans at the top, which is his starting point rather than his conclusion.
eg: chimps don't teach. So what? Killer whales do, so humans aren't the only animals that teach.
Other big statements of supposedly unique human attributes, such as compassion for non-relatives and a sense of history and the future, are also highly questionable. And again, he seems not to be considering much beyond other primates here.
The strongest argument is to do with language, although I think grand statements about the language abilities of others could do with more qualifications until more is understood about other animals' communications. Again back to killer whales - we're only really just beginning to scratch the surface of their behaviour, and it is increasingly clear from their behaviour that they're communicating with one another in ways we don't yet understand. The history of the study of animal behaviour has been one of knocking down one pillar after another of supposed human uniqueness. Fully formed language today is one such pillar. Things such as tool-use or culture used to be, but now very clearly are not.