American democracy has survived for centuries, and has endured great tests. That's a definite positive. I would also argue that our country is fairly stable and nonviolent. Despite the current economy, we are mostly economically successful. I worry about the current infighting in Congress though. This is a definite disadvantage.

The major strength of American democracy has been that it is fairly tolerant and inclusive.  This may sound strange given that the US has a checkered history that includes things like Jim Crow and the Japanese internment in WWII.  However, the US has absorbed more different types of people than any other country in the world.  Its democracy has extended rights to all of them and has maintained a very open attitude towards different races, religions, and political ideas.

The major weakness of American democracy is the fact that people seem to want a "free lunch."  Americans have come to believe that the government can provide all sorts of services without having taxes that are high enough to pay for them all.  This has led to our current situation in which we are floundering, trying to figure out how to get ourselves out of a massive debt without cutting spending or raising taxes.