It's interesting to read this story with the purity codes of the Old Testament in mind, because the woman who has been bleeding is ceremonially unclean (Lev 15:25) and the dead daughter of Jairus is also unclean, and yet Jesus touches both of them. According to my understanding of Old Testament purity codes and first-century practices, wouldn't touching them also make Jesus unclean? The woman with blood only touches Jesus's cloak so I am not sure if this would be enough to make him unclean, but when Jesus "took [Jairus' daughter] by the hand" (Mt 9:25, Mk: 5:41, Lk 8:54) that would seem to make him unclean. According to Numbers 19: 11 touching a dead body made someone unclean. This fear of corpse contamination may be some of the reasoning why in the story of the Good Samaritan the priest and the Levite both avoid the wounded man. Jesus also talks of this defilement when he calls the Pharisees "whitewashed tombs" (Mt 23: 27) in reference to the unmarked graves in the Kidron valley which could within sight of the Temple accidentally render a pilgrim, coming to celebrate Passover, unclean for seven days.
Jesus is not concerned with purity codes, not because he is disregarding the Law, but because just as honoring the Sabbath should not keep him from helping others in need, corpse contamination would not keep him from doing the Father's will of healing. We see in this story that Jesus is willing to touch and be touched by those who society shuns. Jesus does not hesitate to reach out and get his hands dirty for our sake, and his interactions with these two women demonstrate the larger truth of how Jesus, who is perfect, came into the dark and dirty world so that he could restore and save us.
This raises a question about the Law which is not addressed in the Law: if a dead body ceases to be a dead body does anything rendered unclean by that body become clean again? For both the woman with the bleeding and the daughter of Jairus, Jesus took away their uncleanliness. Jesus overcame the source of their defilement and made them clean.
So the answer my earlier question of did these women make Jesus unclean is no. The uncleanness of both women did not make Jesus unclean because he makes unclean things clean. His power to purify trumps any ability to defile. And this is an illustration of the Gospel, Jesus came into this unclean world and not only purifies us according the rules of cleanliness, but he also fulfilled our debt to sin and imputes us with his righteousness. Like I said, Jesus is awesome.
