The Unblemished Lamb on Shabbat HaGadol

How did Yeshua fulfill the 10th through 14th of Nissan, the days of selecting and observing the Passover lambs? Why did Yeshua have to be tamim, without defect or sin? How is what G-d does with our sins in the B'rit Hadashah (New Covenant) different from what G-d did with sins in the Mosaic Covenant?