One of the objections to Christianity that I hear quite often doesn't really come as a challenge to the traditional arguments for God's existence or Jesus' resurrection. It, instead, makes an observation about the followers of Christ and draws a conclusion about the truth of their beliefs based on how well they follow what they say they believe.
This is the problem of hypocrisy in the Church. Many unbelievers look at Christians and see that we all are not perfect and that we sin, quite often, in fact. What gets people is that if someone believes something, then they should be acting like they believe it. They think that if someone's actions are not perfectly in line with what they say they believe, then they don't really believe it. "If someone who says they believe something doesn't actually believe it, then why should I believe it?"
I like how Ravi Zacharias describes this in his book, The Grand Weaver. Zacharias points out that such hypocrisy creates a contradiction in the life of the Christian (Chapter 4). The unbeliever sees this contradiction, and knowing that contradictions are not a part of reality, they may then reject the worldview of the Christian.