You might want to approach this excellent question from the angle of examining the time in which the Constitution was drawn up and then comparing that context to the very different context of today. This is a problem with all Constitutions, as they present themselves as inflexible documents that are not able to change as the times and context changes. So, what is different now about the situation of the USA and is the Constitution still as relevant as it was when it was first adopted?
In light of the many "wars" that the United States is involved in, it would be interesting to look at the Constitution's decree that only Congress can declare war, while the president serves as Commander in Chief. Yet, presidents can engage in short term military engagement under certain circumstances without congressional approval. Should something be done to tighten the control over the president in regards to military action?
Consider the failure to impose term limits for members of Congress. When the Republic was formed, serving in Congress was a matter of temporary public service, whereas now it has become for many a very lucrative lifetime career. Without term limits, the matter of reelection becomes a paramount priority, if not the most important priority. Every major decision is analyzed in terms of how it might affect representatives' or senators' chances for winning another term. Those who are primarily concerned with themselves will avoid making controversial decisions, even if they might be the right decisions. Without terms limits, members of Congress are more vulnerable to being influenced (or bought) by huge financial donations from powerful and wealthy special interest groups.
This totally depends on what you think is right or wrong. Here are some examples that you might think about:
- The president has to be born an American citizen. This has never been a big deal, but it's not (you could argue) really fair. Why should someone like Arnold Schwarzenegger be able to be governor of CA but not president? Looked at another way, aren't all citizens equal? My dad is a naturalized American. What makes him less deserving than someone who was born here?
- Or you could look at parts that are too vague. For example, the First Amendment on religion. What does it mean to say that everyone has the right to "free exercise" of their religion? Can I do drugs as part of my religion? What about if I want to marry more than one woman as part of my religion? What does that clause actually mean?
So those are two parts you can criticize; one because it says something unfair and one because it is too vague.
Oh... one more. What about the part that gives every state two Senators? In the Senate, Wyoming has as many representatives as California even though CA has about 70 times more people. How is that fair?