Greg Koukl offers a very helpful response to this common objection to biblical accuracy, authority and authenticity:
First, it doesn’t follow that because the Bible’s written by men, that it therefore must be in error. Human error is possible, not necessary. If human error were always necessary in anything man said, this challenge would be self-refuting (“suicide tactic”). If all human claims were necessarily in error, then the claim that the Bible was written by men and men make mistakes would also be in error because it’s a claim made by men who err, defeating itself. It is possible for human beings to produce something without errors. It’s done all the time. What is 2+2? What is the formula for nuclear fission?
Second, this is circular reasoning. If there’s good evidence the Bible can be trusted, then the issue of man’s involvement is moot. A simple question illustrates this: “Are you suggesting with this objection that if God does exist, He’s not capable of writing what He wants through imperfect men?” This is hard to affirm. If the answer is “No,” then the objection vanishes. If the answer is yes, then ask, “Did you ever own a dog? Could you get your dog to sit? If you can get a dumb dog to sit, what makes you think an all-powerful God can’t get a man to write just what He wants him to?” If you first establish that the Biblical record can be trusted, then the second problem—human involvement is irrelevant. If God inspires it then it doesn’t matter if men or monkeys did the writing; they’ll still write exactly what God intends.
Another way of stating it: God can’t err; the Bible is God’s Word; therefore, the Bible can’t err, even if men are involved.
Check out Greg's book Tactics for more great apologetic material.