Since mentioning the Judas problem in the introduction, I thought that would be a good place to start. Without doubt, one of the conundrums that non-Christians love to throw at us to "prove" that the Bible contradicts itself is the puzzle of how Judas died.
According to Matthew 27:3-8 we read, "Then Judas, which had betrayed him, when he saw that he was condemned, repented himself, and brought again the thirty pieces of silver to the chief priests and elders, saying, I have sinned in that I have betrayed the innocent blood. And they said, What is that to us? see thou to that. And he cast down the pieces of silver in the temple, and departed, and went and hanged himself. And the chief priests took the silver pieces, and said, It is not lawful for to put them into the treasury, because it is the price of blood. And they took counsel, and bought with them the potter's field to bury strangers in. Wherefore that field was called, the Field of blood, unto this day."
In Acts1:17-19 Luke tells us, "For he (Judas) was numbered with us, and had obtained part of this ministry. Now this man purchased a field with the reward of iniquity; and falling headlong, he burst asunder in the midst, and all his bowels gushed out. And it was known unto all the dwellers at Jerusalem; insomuch as that field is called in their proper tongue, Aceldama, that is to say, The field of blood."
The first thing we will address is the purchase of the field. Matthew says that the priests took the money that Judas threw back at them and bought a field. Luke said that Judas bought it. How can this be reconciled? Well, Matthew, being a tax collector would have been very aware of money and the legalities of this whole field purchase transaction. It is obvious that the priests were the ones who purchased it, but it is most probable, as they considered this money tainted, that they bought it in Judas name, as they would have wanted to disassociate themselves from the entire transaction, and considered the money his. Since someone had to bury him, they bought a piece of property that would have been useless for anything else other than burying people, and decided to use it not only for Judas, but for a potter's field, or place to bury people who had no family or were indigent. Both accounts agree as to the name, "the field of blood". Everyone knew what Judas had done, and this field was called that because it was where he was buried, therefore everyone assumed he had purchased it. Luke may not have known that it was actually the priests who purchased it, as Judas had by all accounts given the money to them, and they buried him in this field. It would have been an easy assumption for everyone to make that Judas had purchased the field himself, as he deliberately killed himself, and most would have assumed he had taken care to provide a burial place for himself. Matthew however knew more of the circumstances than the population at large, and clarified the exact events that transpired.
Now to the more difficult dilemma. How did Judas die? Matthew spends a lot of time telling us about the money transaction, but gives five words to tell of Judas' death - "and went and hanged himself." This makes sense, as Matthew's occupation had been all about money. Luke on the other hand mentions the purchase of the field only in passing as the gain gotten with the price of betrayal. Then he gives more details on how Judas died. This would also make sense, given that Luke was a physician. But the problem still remains, one says he hanged himself and the other says he fell and literally split open with his entrails gushing out. It would at first look seem impossible to reconcile these two things. That is, until you know the missing piece of information.
A number of years ago I sat in church and listened to a guest speaker who had been over to tour Israel. In the course of his sermon, he told us something I never forgot. In the course of his tour, he had visited this area where the potter's field was supposed to be, according to Scripture and local information. One look at this area immediately told him how to reconcile these passages. It seems that there are fields over there through which run gorges. These fields, because of the gorges would not have been all that useful as fields for crops. Therefore purchasing one to use for a burial ground would not be a difficult thing to do and it would use otherwise unusable land in a constructive way. On the banks of these gorges there are trees that grow and hang out over the gorge. It immediately came to this person as to what had happened to Judas. Matthew was correct in that Judas' intention was to hang himself. But how does one easily do that? Get a ladder or stool and find a branch that is accessible, then kick out the ladder or stool from underneath yourself? That seems overly difficult. Is it not much easier to find a tree with a branch that overhangs the gorge, tie yourself to it and jump? That is precisely what Judas did. He thought he was going to hang himself. What he did not count on was that the branch would not support the weight or force of his jump. It must have snapped, plunging him down into the gorge, thereby splitting his body open. Just falling in a field, as Luke says, would never make a body explode apart as he describes. A head injury maybe, a broken limb perhaps, but a simple fall in a field causing the body to literally burst open? No. No way. Only a fall from a decent height would cause that. Matthew was only interested in what Judas intended to do, and as far as he was concerned, since Judas set out to hang himself, that was how he died. Luke on the other hand was a doctor. And just as Matthew was finicky about the details of the money, Luke is finicky that the details of the death be accurate. Judas did not die from being hanged. The branch broke, and his neck may not have been broken. However, Luke can say with absolute certainty that Judas died from the fall and having his insides splattered all over the place. And therein lies the truth and the answer to the "contradiction" of Scripture. If we knew all the missing pieces of these "contradictions", I am sure all of them would as easily be reconciled.