People have all kinds of verses that they claim are "contradictions" in the Bible. They're not. The people who make these claims don't look into them at all and take things out of context, and in turn, think such things as that the Bible allegedly claims insects have four legs. Most of these alleged contradictions can be debunked with a single Google search, but why bother going to all that trouble? I have a blog, and let's save some people the trouble here.
I'm hoping to make a bigger post out of this, but let's just get started.
1. Two different accounts of the origin of the saying "Is Saul among the prophets?" are given in 1 Samuel.
Truth: Later in the Saul story we read that David fleeing from Saul arrived at the prophet Samuel. Saul persecuting David also came there and again came into spiritual ecstasy. By that it seems that David being on the run from Saul was able to escape from him. In this occasion again we read: “Therefore they say: Is Saul among the prophets?” The usual translation, however, is not correct. An imperfect is used in the Hebrew: “Therefore they said: Is Saul among the prophets?” The meaning is not that this saying started here as a common one. Again the people were surprised and repeated the already fixed expression. [Source]
2. Abraham broke the law by marrying Sarah
Truth: The law hadn't been given yet. There was no law forbidding him from marrying Sarah. She was "the daughter of [his] father but not the daughter of [his] mother", so by our standards he shouldn't have married her, but the law hadn't been given yet. He couldn't be held accountable for it, because there was no law yet forbidding it.
3. Jesus wants us to hate our families because of Luke 14:26
Truth: Translation issues. Just like with 1 Samuel. Jesus does not want us to "hate" our families. What it means is that we must put Jesus first, even to the point that it may appear as though we hate them. Matthew 10:37 explains it much more clearly. Jesus commands us to love others, and this is no exception. It's the 2nd greatest commandment, but the 1st greatest commandment is to love God.
4. Numbers 11:20 contradicts Numbers 11:33
Truth: Translation issues once again. Let's get some context going quick. Israel was getting greedy about food. God was giving them food, but they wanted other things and weren't happy with what God was giving them. In Numbers 11:20, it's said that God will give them meat for a month, but in Numbers 11:33, God is said to send a plague while they were still eating it. What this actually means, according to the older Hebrew, is that the plague was sent before the meat was cut off from the people. That is, they ate for a month, weren't done eating it yet, and thus were still eating it at the time that the plague was first sent.
5. 1 Samuel 31:4-6 and 2 Samuel 1:1-10 contradict each other
Truth: The verses in the first passage describe what actually took place. The account given in the 2nd passage about Saul's death is a story fabricated by a random person. Read carefully how 2 Samuel talks about this situation. Among other clues, notice that it never mentions these events transpiring where Saul asked a random Amalekite to kill him. It simply says he relayed the story, not that it actually happened beforehand; the text treats the man's account as words from his mouth, not as an actual historical account of what happened to Saul, as the first passage does. It's really obvious, but something that people don't take the time to examine at all - they see what first appears to be a contradiction, so they make assumptions about it instead of taking things in context. This is the case with tons of alleged issues people have with the Bible - they take random verses that may seem unappealing or contradictory at first glance, but never bother to investigate it at all. It's the same as if someone in ancient Israel had read a prophecy about Jesus suffering, and one about His kingdom never ending. The two only make sense when you take Jesus' entire life, and everything written about Him into consideration; He suffered, and rose from the dead, and now His kingdom never ends. If you take the two separately, of course they won't make sense. To really drive home the point of how counterproductive and unreliable it is to take random verses out of context, read this Bible verse.
These are just a few. I hope to add more later. In the meantime, this website seems to be a good resource if you have further questions.
May God bless you all and guide you according to His perfect will. In Jesus' name. Amen.