Democracy is just the worse (although the most likely and achievable) of the 3 good forms of government.
I think Plato's student Aristotle is more interesting here, not least because I'm regularly susceptible to the old academic claim that The Republic is a satire. In his Politics, Aristotle extends the three categories Plato uses by cross-cutting them with the core value judgement: good vs. bad. I think he was on to the more imporatant part of the analysis here b/c no form of government will work well if the leadership is, um, frakked in the head.
This means a bad democracy is mob rule, such as classical Athens occasionally saw. But good democracy takes advantage of the general tendency of groups to make better decisions than individuals (Aristotle is the first written claim here, the notion is not really scientific, but it is still persuasive--even marketing worth, what with that Web 2.0 natter).
Our president may be the most powerful individual in our nation, but he can't make a single law without congress, and the supreme court can always declare a law unconstitutional.
Sort of. Unfortunately, the executive has extensive authority to establish regulations and can issue executive orders (even secret ones) covering a wide range of gov't activity. Congress is the source of fundamental legislation, but through history they have used that power to delegate *lots* to the executive, starting with the budget process changes early in the 20th and getting much messier through WWII, the Cold War, and the rise of regulatory bureaucracies in the post-war decades.
Perhaps more importantly, the Supremes cannot *always* declare a law or executive action unconstitutional. First, they can't start anything on their own--someone has to bring a suit before them. Second, they really do tend to uphold the judicial tradition of precedent, so their power is rarely as arbitrary as this line makes it sound. There are certainly exceptions to prove the rule, but on the whole they try to remain detached from the short-term flurries of public opinion.
Re "how the next leader is chosen," don't forget that democracy does not require an executive branch at all, much less a singular one. The debates that led to the US constitution included calls for our presidency to be plural, like the executive in some modern US cities and counties (commissions and boards with weak chairs and weak or no mayors).