If there were a clear contradiction in the Bible, that would certainly count. However, I have yet to encounter an apparent contradiction that could not be explained. Addressing all of them is more than I can handle in this space, and there are some fine books that tackle this issue. I'll present one of my favorites, for the sake of this argument:
Do not answer a fool according to his folly, or you will be like him yourself.So, which is it? Answer a fool or not? It's easy to write this off as a contradiction, but let's face it, even a somewhat smart human wouldn't make this kind of error (and it is the same human author, or at minimum the same human editor). What makes more sense is the author (and Author) is making the point that sometimes you need to answer a fool, and sometimes you need to hold your tongue. So, this doesn't qualify as evidence that disproves.
Answer a fool according to his folly, or he will be wise in his own eyes. - Proverbs 26:3-4
So, in Joshua, the Bible says God caused the sun and moon to stand still for an entire day. This passage, at one time, convinced the Church that the sun must go around the Earth (and all sorts of humiliating actions against Copernicus, Galileo, etc. ensued). Now we know that the Earth moves around the sun. Does that mean the Bible is wrong? If it were trying to be an astronomy textbook, then yes; but it's not. Instead, it's describing an event from the perspective of Earth, where it does appear that the sun normally moves across the sky. After all, we do still describe the beginning and ending of a day as sunrise and sunset, though we know the sun doesn't actually do the rising or setting. Again, no sale on disproving evidence.
Maybe the story in Joshua just begs the question. Whether it's the sun or Earth moving is irrelevant; neither just stops in its motion for a day, then starts back up again. That's a lot of kinetic energy to invest, and the laws of physics say it just can't happen. The same thing goes for water standing up on end in the Red Sea, or walking on stormy water. Some believe that's the last nail in the coffin, that science has disproved the possibility of miracles. However, that's just not true. Science has brought us a long way; we once thought phenomena like thunderstorms were an "act of God", but now we know they are explained through natural laws. It doesn't follow, however, that miracle cannot exist. In fact, since science focuses solely on the explanation of the natural, it is silent on the supernatural. We may not observe any miracles today, but that doesn't mean they didn't occur 2000 years ago.
This seems like a funny topic, as it doesn't seem very controversial. I haven't heard of any protests of fundamentalists outside the Weather Channel studio. And yet the Bible does say that God (and not natural law) controls the weather. So which is it? Again, I think some flexibility in thought is needed here. God could control the weather through natural means. It might mean God sometimes steps in and overrides natural law to accomplish his ends. Either way, I don't think this is conclusive.
The existing set of evidence that I believe makes the best case for disproving Christianity is macro-evolution. That's what I'll write about in my next post in this series.