I think that my biggest concern with Communion isn't necessarily that we don't do it "right", but rather that it has been weaponized to separate Christians from one another. How often is Communion closed to anyone who isn't the "right" kind of Christian. You'll even hear denominations speak of other denominations that they're "in Communion with". Sadly, all those who put up barriers to Communion outside of that which is prescribed in Scripture place roadblocks to Christian unity.
1 Cor 3:1 But I, brothers, could not address you as spiritual people, but as people of the flesh, as infants in Christ. 2 I fed you with milk, not solid food, for you were not ready for it. And even now you are not yet ready, 3 for you are still of the flesh. For while there is jealousy and strife among you, are you not of the flesh and behaving only in a human way? 4 For when one says, “I follow Paul,” and another, “I follow Apollos,” are you not being merely human?
5 What then is Apollos? What is Paul? Servants through whom you believed, as the Lord assigned to each. 6 I planted, Apollos watered, but God gave the growth. 7 So neither he who plants nor he who waters is anything, but only God who gives the growth. 8 He who plants and he who waters are one, and each will receive his wages according to his labor. 9 For we are God's fellow workers. You are God's field, God's building.