(Taking up this title from over two years ago, not having any recollection of what it was supposed to be about at the time.)
The pursuit of happiness as a constitutional right is just wrong.
What effect could it have, except to develop the misconception that happiness is something that is pursued, and even worse, something you have a right to? Happiness is an emotion, like anger, frustration, sadness. It cannot live in a vacuum without becoming one. It gets it value precisely in its contrast to sadness/anger/frustration.
Rather, happiness should be considered a side effect. The real pursuits should be for Purpose, Goodness, Truth, Knowledge, Unity. When we achieve these, happiness is just the side effect.