The existence of a contradiction is largely a matter of perception and usually indicates a lack of understanding as opposed to the actual existence of a contradiction.

-- skip this if you don't at least appreciate math --
I'm a physicist and a programmer, and so, speaking mathematically, the existence of a true contradiction within any formal system makes the system "incomplete" and hence, useless. Far worse, the existence of a contradition allows any given statement to be proven both true and false and ultimately destroys all meaning within the scope of the system.
-- back to the real world --

In the real world, filled with people and flawed communication, contradictions are aprehended all the time. When something is communicated, as in the constitution, there are only two kinds of contradiction. (That I can think of.)

One kind is the serious kind caused by the communicator who either makes a mistake in what he is communicating (communicates what he did not intend), has a flawed and inconsistent view on the topic at hand, or has lied and thus intends to pass off an inconsistency undetected.

The other kind of contradiction is only aprehended and does not really exist. This results from the flawed understanding of the listener either in perceiving what is spoken, or in the set of facts he tries to compare what is being communicated against.

When the founding fathers (also called "the framers") laid the foundation for a republic on the North American continent, they wrote about its fundamental structure and communicated it via the United States Constitution. It was, however, only a structure intended to serve as a starting point to be modified by the people via the legislative branch of the government and only the legislative branch. (That's what it means to legislate.) It is well known that many of our country's founders desired greater protections and greater equality than was originally set forth in their document, but they agreed that it was a good starting point, as it was.

Thus, when it was finally possible to abolish slavery, it was done via an amendment created by legislative authority.

However, there are numerous rights which seem to exist today (the right to privacy, the right to an abortion, and others) which can not be interpreted from the constitution unless done so via the second kind of contradiction. Thus judges have invented rights which were never in the US Constitution. They say a state can not do something when there is no legal reason why not (Roe v. Wade) and they say a state can do something when it is plainly written they can't. (Kelo v. New London)

This is not just resolving contradiction or uncertainty (for which the court has invented many very reasonable "litmus tests"). This is the invention of what was not there before and the overturning of what is plainly written. That is called legislation. Legislation is done all the time by senators and city council men and the like. However, these are people we voted for. They are our representative. I did not get to vote on Rehnquist and I did not get to vote on Ginsberg. Not only that, but I can't do anything to get rid of them either and so, when justices start to circumvent the legislature and write their own laws in the books of court opinion, it is a very dangerous thing. If we amend the constitution to protect people's property rights and they decide to ignore the amendment by redefining "public use" to fit their own Alice in Wonderland definition rather than the one intended, it is a very dangerous thing. And this "spirit of the law"; this spirit of judicial nonarchy (nine kings), is the same spirit which invented the right to abort.

Roe v. Wade wasn't just some balancing act over conflicting rights and responsibilities. I recommend reading the decision. In summary it says "The hipocratic oath is obsolete (!!!) thus states don't really need to be worried about abortion, thus we'll use the right to privacy [which we invented and hope you wont notice] to declare early abortion restrictions illegal." Not only should we be scared to death that the supreme court thinks that the hipocratic oath is obsolete, but they lied to us. They performed the first kind of contradiction in the worst way. They intentionally snuck a contradiction under our nose.

Now if one really thinks that abortion is a good thing, an amendment would have taken longer, but it wouldn't have been as messy as the nonarchy method and it wouldn't have led to Kelo v. New London either. The delays, however, probably would've annoyed abortion's proponents and it probably never would have happened because the people wouldn't have wanted it. But that only matters if one cares about having the right to abort more than they do about the people's right to representation.