In regard to the story of Jephthat, you say that God did not approve of the sacrifice of his daughter. How can you say this? Jephthat was granted military victory, the Judgeship of Israel, six years (I think) of further life and a peaceful death. He was not punished, in contrast to the punishment so many others received for comparatively trivial sins, e.g. for his "disobedience" at Meribah, Moses wasn't permitted to step foot in the promised land. For his actions against Uriah, David was punished with his family's treachery and shame. Heck, a man was even struck down for gathering wood on the Sabbath. How does Jephthat not only get away with this, but get rewarded?
Yes, Jephthat was granted all of that, but none of it was any kind of reward for the killing of his daughter. God disapproves of human sacrifices, yet Jephthat (disobeying God) promised to sacrifice the first person he met upon returning home. Because of this careless and ungodly promise, Jephthat was forced to kill his only child. I wouldn't call the loss of your only beloved child a 'reward', would you? Jephthat clearly regretted having made his vow in 11:35. Besides, Judges 11:40 clearly says that the sacrifice of Jephthat's daughter was lamented for four days every year by the daughters of Israel. If it was something God condoned, why would the daughters of Israel be lamenting it?
"Well, if God didn't condone it, then why did he let Jephthat win the battle, thereby ensuring the fate of the daughter (or whichever person came out to greet him)."
Much more was at stake in the battle than the daughter's life. It can be assumed that had they lost the battle, many more Israelites would have died.
"And how could God condone punishing one person (the daughter) for another person's sins? That doesn't seem very godly."
God wasn't the one who killed her. It was Jephthat. God never asked Jephthat to make the vow, and God never asked Jephthat to carry it out.
"And why wasn't he struck dead immediately after committing this crime, as so many others in the OT were, and for far less serious crimes."
Because God wanted a lesson to be taught to Jephthat. Striking him dead wouldn't have done it.
"You can't deny that Jephthat was granted many rewards after the sacrifice,"
Yes, but the rewards were for other things. Jephthat did many good things on God's behalf, and was rewarded for them. He also did at least one terrible thing (promising a human sacrifice to God), and lost his daughter because of it. Rewards for good things and losses for bad things is the logical way that it should work. Jephthat learned his lesson, and from his example, many others learned not to make promises to God that are against His will.
"and the fact that the women of Israel lamented the tragedy of her death has nothing to do with whether God condoned it or not."
What do you mean? Why would the daughters of Israel be lamenting something that was good in God's sight?
"Ok, you made a lot of good points and I can accept it. Thank you. Maybe you can help me with some other things I'm struggling with. Mark 2:23 quotes Jesus referring to the book of Samuel (1 Samuel Chapter 21 verse 1) where David eats the bread of the priests. Mark quotes Jesus as getting the name of the priest wrong and then referring to David giving the bread to his companions, when the text of Samuel said that David was alone! How could the Bible be inerrant when it quotes Jesus as not knowing Scripture?"
Mark said that Jesus went to [the house of] God "in the days of" Abiathar the High Priest, not that he met with Abiathar. Abiathar was the father of Ahemelech and was still alive at the time. Just like if I said something happened "in the days of George Washington", that doesn't mean Washington was right there when it happened. As for his companions, read 1 Samuel 21:4-5. Ahemelech and David clearly talk of sharing the bread with David's men. They aren't with him at the time that he is meeting with Ahemelech, but they're nearby and he is clearly planning on sharing it with them.
"Then there is Matthew 27:9-10 in which Matthew quotes a verse from Jeremiah which does not exist! These are only two of the many problematic verses which are trying my faith."
It's probably referring to the prophecy in Zecheriah 11:12-13. Though it is called the book of Zecheriah, the ninth, tenth, and eleventh chapters were written by Jeremiah.
I don't know if you've seen it, but I have a contradictions site here. I addressed both of those to some extent, though I admit the site's a little difficult to search through and my answers are rather brief. Another very good site which goes into detail on each of your concerns is www.tektonics.org.