ANSWER: Even the most severe critics of the Bible do not say that it contradicts itself all of the time or that it is full of errors. There are, however, some legitimate questions about accuracy that can be raised.
As a general point, when tackling apparent contradictions and errors, it pays to consult such books as John W. Haley's "Alleged Discrepancies of the Bible," and Gleason Archer's "Encyclopedia of Bible Difficulties." Many things that seem to contradict themselves are hardly new discoveries. In fact, some have been known for a long time, even for centuries. The responses of conservative Christians (or, if applicable, Orthodox Jews) should be consulted by the open-minded before skeptics begin their criticisms.
Many alleged Bible contradictions can be dealt with as being scribal errors, especially when concerning numbers in the books of Samuel, Kings, and Chronicles. For example, 2Samuel 8:4 states that David took 700 horsemen while 1Chronicles 18:4 states he took 7,000. Another scribal error occurred when in one place it states Jehoiachin was eight years old when he ascended the throne and another place states he was eighteen.
Gleason Archer, when explaining 1Samuel 13:5, which has an apparent scribal mistake in it that increases the number of chariots the Philistines had, said the following. He stated, "The accurate preservation of statistics and of the spelling of proper names is notoriously difficult in manuscript transmission, and 1Samuel has more than its share of textual errors. But the doctrine of scriptural inerrancy guarantees only the original manuscripts of Scripture as preserved from all error; it does not guarantee absolute trustworthiness of all copies . . ."
Other places where the Bible seems to contradict itself occurs in Matthew, where we read that Jesus met two blind men. In Mark and Luke, we only read about one blind man meeting him. In Matthew and Mark, we read that Jesus went to pray alone three times in the Garden of Gethsemane, whereas, in Luke, we read that he went alone to pray on one occasion. In both of these instances, the apparent inaccuracies can be explained because the events in one account could be contained in the other.
The apparent discrepancy between John 5:31 and John 8:14 is more interesting than those above. Jesus was referring to the Old Testament law that two or three witnesses were necessary to convict someone of a crime (Deuteronomy 17:5, 19:15). Jesus didn't mean what he was saying wasn't "true," but rather that it wasn't "valid" under these rules of evidence if (hypothetically speaking) no one else could bear witness to its truth. The use of that little but crucial word "if" makes what he said into a hypothetical. Since, however, the Father also bore witness to what Jesus bore witness to, it would pass legal muster (cf. John 5:32, 37; 8:18).
Critics of the Bible can point to places where the text seems to contradict itself and, without doing any futher research (and lacking faith), justify their position that the book is not inspired and cannot be trusted. What they have a harder time doing, however, is explaining away the places where Scripture predicts the future and the events it predicts HAPPENS! Such predictions include Daniel's prophecies regarding the history of Persia. It also includes his inspired predictions regarding not only Alexander the Great's Greek empire but also how his generals and their descendants would fight after his death.
The remarkable accuracy of Bible prophecy is so amazing that higher critics are left with turning them into mere texts that write about events that have already occurred. This is done in spite of the fact that the Biblical texts in question can be dated far sooner than the events they predict. To research other ways Scripture seems to contradict itself, you may wish to get a copy of Josh McDowell's "Evidence That Demands a Verdict" or other like book.