Since Passover falls during Holy Week this year, it is most appropriate to consider possible connections between the Passover seder and the Christian Eucharist.  (And even if the Last Supper did  not take place during a seder, as some New Testament scholars maintain, Passover was definitely in the air.)

A worthy effort in this direction is Jesus and the Jewish Roots of the Eucharist by Roman Catholic scholar Brant Pitre (Doubleday 2011).  Pitre documents parallels between the Eucharist and a number of Jewish concepts such as messianism, Exodus, manna, the Bread of the Presence, and the paschal lamb.  What Jesus and his followers did was not to discard the seder but to reinterpret it in a radically new way.  Examples are found on pp 70-74.

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...the Last Supper was also different--radically different--from an ordinary Passover meal.  Any ancient Jew, including the apostles, could easily have seen this.  For one thing, most Passovers were celebrated within families, with the father leading and acting as head.  At the Last Supper, by contrast, Jesus acted as host and leader of the Twelve, even though he was not the father of any of the disciples.  Even more, at an ordinary Passover, the focus was on God's covenant with Abraham, the exodus from Egypt, and the entry into the promised land of Canaan.  Yet Jesus spoke instead of the "new covenant", prophesied by Jeremiah to be fulfilled in the age of salvation...Perhaps most significant, at an ordinary Jewish Passover, the entire liturgy revolved around the body and blood of the sacrificial Passover lamb.  First, the lamb would be slaughtered, and the priests in the Temple would pour out the blood of the lamb on the altar.  Then the Jews would bring the body of the lamb from the Temple to the Passover meal, and the father would explain its meaning at the meal.  Yet at the Last Supper, Jesus did something entirely different.  With his words of explanation, he shifted the focus away from the body and blood of the Passover lamb (of which there is no mention), and turned it toward his own body and blood.

... Along the same lines, before the Temple was destroyed, the climax of the Passover sacrifice was the pouring out of the Lamb's blood by the priests in the temple...[Jesus calls the Passover wine "my blood of the covenant which is poured out for many".]...When we compare Jesus' actions to these ancient Jewis traditions, it doesn't take much imagination to figure out his point.  By means of his words over the bread and wine of the Last Supper, Jesus is saying in no uncertain terms, "I am the new Passover lamb of the new exodus.  This is the Passover of the Messiah, and I am the new sacrifice".