The above youtube video does not describe exactly what each half does, but rather what each hemisphere specialize: a generalization.
The video does an excellent job in pointing out the linearly popular approach to problem solving and thinking.
In America, the linear way of thinking and problem solving (or the "faithful servant" model) is praised, while the non-linear way (the "intuitive mind") is ignored or discarded.
The advantages of the clip lie in the credentials of the man presenting the ideas: a psychiatrist.
However, the weaknesses lie in the lack of evidence or empirical data.
Although his claims may be true, it seems that much of what he is saying is based on philosophical claims: going into the world of "what the world should be" rather than a purely scientific "what the world is."
Of course, ironically, this approach is linear in itself.
He even addresses said point:
"Pascal - 'The endpoints of rationality is to demonstrate the limits of rationality.'"
In other words, although his claims involve logic and reasoning (thus making them valid), they are not presented with evidence, making the credibility of the video lose some of that value.
Another logical fallacy examined here is the confirmation bias. Obviously, this presentation is a personal voice of the speaker ("I", "me", etc.), so we can safely say that what he discusses is a personal opinion, and not necessarily a scientific claim. He does not rule out rival hypothesis, either, so we can say that this clip is an instance of where someone is interested in saying what they wanted to say: not actually search for truth.
On a side note (just for fun), here are a few lines that I enjoyed:
"For imagination, you need both hemispheres; for reason, you need both hemispheres."
Left - denotative language; abstraction yields clarification; general in nature; lifeless (fixed, isolated, static)
Right - by contrast, offers changing, individual, implicit, incarnate, living, etc. (within the context of the real world)
Pascal - "The endpoints of rationality is to demonstrate the limits of rationality"
Left brain model - "This model is entirely self consistent partly b/c it's made itself so."
Einstein - "The intuitive mind is a sacred gift, and the rational mind is a faithful servant"