One of the "worldview tests" that Kenneth Samples discusses in his book on worldviews, "A World of Difference", is a test for internal consistency. Any worldview that claims to accurately reflect reality (be true) must maintain consistency among its beliefs. Truth cannot conflict with truth. So, if a worldview were to say that 2+2=4 and that 3x2=5, it would have a serious problem. The fact that the second claim is false has no bearing on the truth of the first claim, it only has bearing on the truth of the worldview as a whole. Any worldview that contains two contrary beliefs that cannot be resolved within the framework of the worldview without creating more contrary beliefs must be discarded.
An apologist for any worldview (Christianity, Naturalism, Islam, etc) must be able to reconcile seemingly contradicting beliefs if they wish to maintain the claim that their worldview is true. If they cannot resolve the conflicts, then they run the risk that the person they are trying to convince will look elsewhere.
An apologist may also take it to the next level, and be aware of the inconsistencies in the competing worldviews and how to demonstrate that they are, in fact, actual inconsistencies (versus just paradoxes). This is where it becomes quite important to be aware of and avoid the "straw man" fallacy (see my post "This Argument is Full of Crap!") and Greg Koukl's new book Tactics: A Game Plan for Discussing Your Christian Convictions.
There is another way that a worldview can be inconsistent. It is inconsistency with the behavior of the person defending it. Now, I am well aware that it is not a valid, logical test for truth to look at the adherents' behavior, but many people do (some people even know its illogical, but still claim it is logical to avoid the implications of the worldview they are opposing).
This probably applies more to Christianity than the other worldviews. Unfortunately, today's Church has received the stereotype of being "hypocritical" in the eyes of the secular world. Of course, I am not going to deny this for one second. What I am going to say is that the Church's behavior has drastically damaged its ability to witness to the secular world. This also has an even worse effect if the Christian is discussing one-on-one with a person and behaves in a way that is against what he is "preaching".
I will address the Christian behavior issue more in two posts called "What's Up With Atheistic Evangelism".
I have recently written more about the consistency among disciplines in my series about Cumulative Cases.