How much should the ancient Near Eastern setting of the Mosaic Law influence our application of the law in our own lives today?

The reader of the Old Testament accounts and specifically the Mosaic Law MUST take into account the culture in which that text was written in order to fully understand it. So many practical things are covered in the Mosaic Law that dealt with specific instances of wrongs, sins and even what to eat that were specific to the culture and the time period.
Exodus 21:28-32 speaks of a bull goring a man or woman that causes that person to die. If the bull has done it for the first time and no one knew that the bull had that tendency, the bull must die and the owner has no responsibility. However, if the bull had been known for goring and the owner had been warned and the owner takes no precaution in order to prevent it from happening again, the owner is held responsible and BOTH the bull and the owner must die unless the owner has the opportunity to redeem his life by paying what is demanded. I liken this to owners of dogs today. I can't say that we got this law or way of acting specifically from the Mosaic Law, but it make sense. We don't own bulls...but we do own dogs....pretty easy application.
Exodus 22:16-29 speaks of various social responsibilities that we can read today and not be able to make heads or tales out of unless we learn a bit of the culture. This passage can be read word for word and not be heeded because we don't see the SPIRIT of the law that is here. God is worth our best. We don't necessarily give our firstborn children to God, but yet we do give Him our hearts...we are to give Him our BEST. God delivered the firstborn in the Passover...the people of Israel are God's chosen, His firstborn. The firstborn belonged to God because of the salvation given to them as they left Egypt. Our "firstborn" or the BEST of us now belongs to God because of the salvation afforded to us through the gift of Jesus Christ on the cross! What a parallel and what a gift given!