A constitutional democracy is the very best form of government, in my opinion, but it certainly has some disadvantages. One is slowness, and another is the risk of choosing poor leaders.
Democracies are notoriously bad at moving quickly in any number of ways. In the United States, which is the democracy with which I am most familiar, legislation is a good example of this. At the federal level, it takes over 500 people, representatives and senators, to pass a law. Rules are built in that are meant to ensure that this process is informed, intelligent, and thoughtful, for example, requiring a committee to consider potential legislation before it is voted upon by all. But these rules slow up the process incredibly, delaying proposed legislation for months and sometimes years, even aside from all the political machinations that can and do create delays. Another example of the slowness in a democracy is built into the nature of democracy, which requires that change in leadership must be accomplished by way of the election cycle. If the people in a democracy are unhappy with those elected, they are stuck with those people for the remainder of the term. Impeachment or recall are processes seldom used. So, change is slow in a democracy.
There is an erroneous belief that people will vote intelligently and in their best interests all the time, choosing the very best in leadership, but history has taught us that this is not necessarily true. There are many instances in history in which duly elected leaders have turned out to be dreadful leaders. Egypt comes to mind as one example, and there are countless others. The United States is frequently in a quandary when it goes about the world promoting democracy and is then less than thrilled with the peoples' choice. In fact, the United States itself has some striking examples of people not exercising their right to vote particularly intelligently. So, a significant disadvantage in a democracy is voting in bad leaders.
Having said all of that, it should be noted that these are disadvantages we probably do not want to eliminate or are those that can be militated against. Slowness in legislation or change in leadership has some desirable effects as well, deterring decision-making that is too hasty and providing for a stable change in leadership. The alternative seems worse to me, hasty decision-making and terms too short to accomplish anything. The second can be guarded against with a good education of the voting populace, something that clearly needs to be worked on in the United States.