So many people seem to think that the Bible is full of contradictions. They are, unfortunately, deceived. The Bible is inerrant, and can be shown such. Most supposed contradictions are rather easy to explain with just a little bit of logic. A few are obviously not contradictions unless someone desires to see them as such. Some are more difficult, but not one is impossible. So, every once and a while, I will explain some supposed contradictions in God's Holy Word.
- "Contradiction": Who was Joseph's father, Jacob or Heli?
- Base Passage: "And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ." – Matthew 1:16
 - Conflicting Passage: "And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli." – Luke 3:23
 - Inerrancy: Most people agree after studying the passages that translation, not the Bible, is the issue. In Jewish culture, son-in-laws were called sons rather often. It is generally agreed that Luke traces the biological ancestry of Jesus, which Matthew traces the legal ancestry. Thus, a more accurate rendering of Luke 3:23 would read, "…which was the son-in-law of Heli."
 
 - Base Passage: "And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ." – Matthew 1:16
 - "Contradiction": Was Abraham justified by faith or works?
- Base Passage: "For if Abraham were justified by works, he hath whereof to glory." – Romans 4:2
 - Conflicting Passage: "Was not Abraham our father justified by works, when he had offered Isaac his son upon the altar?" – James 2:21
 - Inerrancy: This is an example of removing a verse from context. In James 2, James speaks of how faith is proved through works. Without works, there is no evidence that faith exists. Thus, James was pointing out that Abraham proved his faith through works, and thus he was justified.
 
 - Base Passage: "For if Abraham were justified by works, he hath whereof to glory." – Romans 4:2
 - "Contradiction": How many sons did Abraham have?
- Base Passages: 
"By faith Abraham, when he was tried, offered up Isaac: and he that had received the promises offered up his only begotten son…" – Hebrews 11:17.
"And he said, Take now thy son, thine only son Isaac, whom thou lovest, and get thee into the land of Moriah; and offer him there for a burnt offering upon one of the mountains which I will tell thee of." – Genesis 22:2. - Conflicting Passages: 
"And Hagar bare Abraham a son: and Abram called his son's name, which Hagar bare, Ishmael." – Genesis 16:15.
"For Sarah conceived, and bare Abraham a son in his old age, at the set time of which God had spoken to him. And Abraham called the name of his son that was born unto him, whom Sarah bare to him, Isaac." – Genesis 21:2-3.
"Then again Abraham took a wife, and her name was Keturah. And she bare him Zimran, and Jokshan, and Medan, and Midian, and Ishbak, and Shuah." – Genesis 25:1-2. - Inerrancy: This one is so easy that there are two possible good explanations. For one, God could have been calling Isaac Abraham's only son because he was the only son God had intended and he was the only son of promise. It could also have meant that Isaac was, in Abraham's eyes, essentially his only son, and he did not seem to care much for Ishmael.
 
 - Base Passages: 
 - "Contradiction": Did Jesus baptize people, or did His disciples?
- Base Passage: "After these things came Jesus and his disciples into the land of Judaea; and there he tarried with them, and baptized." – John 3:22
 - Conflicting Passage: "When therefore the Lord knew how the Pharisees had heard that Jesus made and baptized more disciples than John, (Though Jesus himself baptized not, but his disciples…)" – John 4:1-2
 - Inerrancy: These two verses are very close to each other, only separated by a short speech by John. Thus, it only makes sense that John 4:2 clarified the previous statements that Jesus was baptizing by saying it was actually His disciples (this becomes obvious when you include John 4:1, which is the reason, I believe, that the site I found this on excluded John 4:1).
 
 - Base Passage: "After these things came Jesus and his disciples into the land of Judaea; and there he tarried with them, and baptized." – John 3:22
 - "Contradiction": Is God all-powerful?
- Base Passages: 
"Is anything too hard for the LORD?" – Genesis 18:14.
"Behold, I am the Lord, the God of all flesh: is there anything too hard for the Lord?" – Jeremiah 32:27.
"With God all things are possible." – Matthew 19:26 - Conflicting Passages:
"And the Lord was with Judah; and he drave out the inhabitants of the mountain; but could not drive out the inhabitants of the valley, because they had chariots of iron." – Judges 1:19.
"And he could there do no mighty work, save that he laid his hands upon a few sick folk, and healed them." – Mark 6:5.
"It was impossible for God to lie." – Hebrews 6:18. - Inerrancy: No feat is beyond the sovereignty and ability of God. However, some things are against His character. He cannot violate His own character: that would be inconsistent, make Him imperfect, and thus He would not be God. As God, He must stay true to His character. That is not a limitation of His power. Doing anything wrong is not good, and God is good, so by definition He can do no wrong. One can be capable of anything but still limited by his character.
God was not the one who could not drive out the iron chariots. That was Judah. God was with Judah and gave him much victory, but God did not grant him the power to remove the iron chariots. Maybe Judah lacked faith, or maybe God had another plan. Regardless, the lack of power was on Judah's part.
Jesus could not do any mighty work in Galilee because of a character issue. The people of Galilee's hearts were far too hard to accept Jesus, so it would be increasing their condemnation to show them any mighty works. Jesus would never choose to increase one's condemnation without cause.
It is impossible for God to lie for two reasons. First, God is perfect, and lying is wrong, therefore lying is against His character. Second, His words create reality, as the story of Creation reveals. Thus, if God even tried to lie, reality would change in the past, present, and future so that His words would be true. 
 - Base Passages: 
 
I would love to do more, but these are all I will address for now. This should show, however, a good amount of how ridiculous most Biblical "contradictions" actually are. The Bible is inerrant. It is that simple.