At times like the Easter season, apologetic issues receive more attention than they normally do. A couple of common objections to Christianity came up on two radio programs I recently heard.
One came up during an interview with Lee Strobel on a local Christian radio station. The interview was about the evidence for Jesus' resurrection. An agnostic called in, and one of his objections was that there are "hundreds" of years between Jesus and the earliest documents written about Him or the earliest extant copies. Even critics who are more knowledgeable of the subject often object that our copies of the New Testament, even the manuscripts we have from the second century, aren't early enough or are unreliable for some other reason. Last year, I did a three-post series summarizing some of the evidence for the reliability of the textual transmission of the New Testament: here, here, and here.
A caller to Michael Medved's program yesterday raised the common objection that a Christian belief originated at the council of Nicaea. Much of what the caller said was incoherent. She spent a lot of her time arguing that Jesus didn't exist. Apparently, she was suggesting that Christians derived their idea of a historical Jesus from Nicaea. Or maybe she had something else in mind. Other critics claim that the New Testament canon was first delineated at Nicaea, for example. A lot of things get attributed to that council, and other councils are sometimes mentioned. Usually it's a council in the fourth century that supposedly settled the canon, changed the text of the New Testament, etc. Here's a post from last year on the relationship between the New Testament and early councils.
And here's a thread about the implausibility of theories involving widespread corruption among the early Christians (widespread textual changes, widespread suppression of opponents, etc.). Read the comments section of the thread, since there's a lot of relevant material there as well.