To tell the truth, the video wasn't very good. Lessig presents a complex argument and some solutions, and those are best done in book form, so I checked out the book from the library. This is an important book if you're an American citizen.
Lessig argues what many of us who've watched the political process for the last 20 years know: Congress is broken. Not just broken when it's owned by Republicans or Democrats, but broken no matter who controls the house and/or the senate. The problem is that of money, and he traces the history of how it's happened: campaign financing has turned campaigning into a full time job, because of the amounts of money required. While bribery is outright illegal, a lot of the result is that Washington D.C. has become a gift economy, where "gifts" buy attention as well as time.
Lessig points out other places where Congress has become corrupted by money, and then details several potential solutions, none of which seems very probable to me (seriously? A constitutional convention? It's more likely that a morally upright billionaire could ride in and save the day). However, this book was written before the Occupy Wall Street movement, and if he can persuade the movement (as well as most of the American people) that this is at the root of the problem, there's a real chance we might have real elections and an ability to actually affect outcome so that we can have a government of the people for the people and by the people again.
The big problem with Lessig's book is that he's not a historian. There have been previous times when the Republic has become as corrupted, for instance, during the Gilded age. It took an extraordinary man (FDR) and a world war to get us out of it, but it would have been interesting to see an analysis of how it happened and how.
In any event, I think the book's way more interesting than the presentation, and deserves every voter's attention. While you might find the book a slog, especially if you start reading the book already convinced that Congress is corrupt, you'll still find something new every chapter. Recommended.