The documentary itself should be nominated for the Barry Norman Awards for the Preservation of the Obvious. If we desire things that we feel ought to be within reach but aren't, we are unhappy. If we meet our expectations (either because we have oodles of money, or have low expectations), then we are happy.
The only bone I have to pick (apart from the fact that it took two hours to draw those conclusions) is the contention that we will be happy by ignoring what others think of us. At a certain level, this is fine, but we do not live in isolation. One of the other great plagues of our time (according to Frank Field and Reichsminister Blunkett) is antisocial behaviour. Surely this is, in some sense or other, the result of not caring what others (outside of an immediate social circle) think of us, or how we impinge upon them? And yet, by the status anxiety argument, these people are the most unhappy because they live with the greatest relative deprivation, and see others climbing a social ladder that is beyond them. I suspect the program's thesis only stands from a chattering classes viewpoint. How ironic.