There have been egregious applications of slavery throughout history which have dehumanized people (often through racist justification) by arbitrarily deeming them property of another person. From my understanding, slavery in OT Jerusalem was not like that. It wasn't ethnically-based (Jews were often slaves of Jews), and it was temporary. It was more of an indentured service-type arrangement in which the slave settled his real debt to his slave master.
Regarding the laws of Isreal, I think it's important to realize that there are three categories of law:
1) the moral laws being a sort of universal trascendent set of standards (summarized by Christ as first, love the Lord your God with all your heart, soul, mind and strength, and secondly, love others as you love yourself...once we have those down pat, we should be good to go ;) )
2) The civil laws in many ways were application of moral standards, but in some ways were not nec. so. These, I think, are what set the nation of Israel apart. As God's chosen nation, they were the standard-bearers of his Word and were to set an example as an (imperfect) version of a holy nation. In the old testament, converts became Jews and so they were expected to uphold the civil law of Israel. In the New Testament, though, the gospel went forth to all nations; instead of bringing people into Judaism, the Gospel transcended national identity (there is neither Jew nor Greek). So gentiles were not expected to behave as Jews -- though there was some considerable strife amongst the apostles here in the begining. (To be fair, they weren't expected to behave as Gentiles, etiher) The civil laws of Israel were not longer applicable, per se. to the Christian. Civil law is still an applicable concept, but we can't expect secular nations to adopt the same codes as ancient Isreal.
(I would note here, too, that there is a distinction between an individual application of the law, and the State's. The State had authority to mete out justice in ways the individual did not. For example, I would contend (though honest arguments can be had regarding this) that the death penalty is a perfectly valid application of state justice which is consistent with Bibilical teachings, becasue the State has the authority to "wield the sword" in ways in which the individual does not.)
3) The ceremonial law was the law of the temple and the rituals of sacrifice for atonement (see: Leviticus). The book of Hebrews addresses the cessation of sacrifices. (esp: Hebrews 10:17-18), but basically, as moral laws were inevitably broken, the priests had been instructed to perform sacrifices on behalf of the people. Some of these were rather complex and precise, and there was a good deal of instruction surrounding these processes. When Jesus -- referred to as the Lamb of God -- died as the ultimate atoning sacrifice, these practices were identified as "shadows" which had not offered atonement in and of themselves, but rather pointed to a coming atonement found in Jesus. These prepared the people's minds for the signficance of what Jesus had come to do. Once he atoned for the sins of the world, the cermonial sacrifices were not only no longer needed, but also borderline blasphemous (at least by my reading) as they suggested a certain need for continued atonement beyond Christ's shed blood.
In many ways the civil law and the ceremonial law went hand-in-hand as specifics of Israel. As a nation, they were particularly shown two things with these laws which prepared them for Jesus. 1) Ultimately the standard for holiness is not going to be achieved by giving man a law...no matter how simple the law was (see: Garden of Eden) or how complicated and nuanced it might be (see: Deutoronomy) people managed to break it...the law reveals how deeply sinful man, but it does not save him (see: Romans 3:19-21 esp.) 2) also, the consequences of sin against God -- the Lord of all --are not trifling. Atonement requires the shedding of blood...either the blood of the lawbreaker or a substitute.
Once Jesus came and both upheld the law and died for those of us who didn't, the presentation changed a bit, though the story and flow remains necessary to set the stage. Ironically (maybe?), Jesus actually revealed a stricter moral law (see: Sermon on the Mount) which challenges man to weigh his thoughts and desires more than just his outward actions, but he also revealed a grace that saves inspite of our trangression from the law. Our disobedience isn't simply swept under the rug, but, instead justice was served when "[f]or our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God." (2 Corinthians 5:20-21 ESV) As we come to understand the grace that is offered to us as sinners, it becomes natural to extend that grace towards those who wrong us.
Bearing in mind the distinction between individual application and corporate application, and understanding our universal need to grace, I think that's how things like "eye for an eye" (state, civil law) can be compatible with things like "turn the other cheek" (individual, moral application).