Here are some insights from William Barclay, Letters to the Corinthians (2d ed.; Edinburgh: The Saint Andrew Press, 1956)
On 1 Cor 1:17 and whether Paul relegated the importance of water baptism:
It is not to be thought that Paul is belittling baptism. The people he did baptize were very special converts. Stephanas was probably the first convert of all. (1 Corinthians 16:15); Crispus had once been no less than the ruler of the Jewish synagogue at Corinth (Acts 18:8); Gaius had probably been Paul’s hose (Romans 16:23). The point is that—baptism was into the name of Jesus. (p. 17)
On knowledge of the Spirit in 1 Cor 2:6-9:
But Paul insists that this special teaching is not the product of the intellectual activity of men; it is the gift of God and it came into the world with Jesus Christ. All knowledge is given by God. It is the result of the seeking spirit of man meeting the revealing spirit of God. (p. 30)
Paul references a previous letter to the Corinthian church in 1 Cor 5:9
It appears that Paul had already written a letter to the Corinthians in which he had urged them to avoid the society of all evil men. He had meant that to apply only to members of the Church; he had meant that wicked men must be disciplined by being ejected from the society of the Church until they mended their ways. (p. 52)
The Theology of the Eucharist (1 Cor 11:23-34)
“This is my body,” He said of the bread. There is one simple fact which precludes us from taking this with a crude literalism. When Jesus said this He was still in the body; and there was nothing clearer than that His body and the bread at the moment He said this were quite different things. Nor did he simply mean “This stands for my body.” In a sense that is true. The broken bread of the Sacrament does stand for the body of Christ; but it does more; to him who takes it into his hands and upon his lips with faith and love and warm devotion, it is a means not only of memory, but of living contact with Jesus Christ. To a stranger, to an unbeliever, to a mocker, it would be nothing; to a lover of Christ it is the way to the presence of Christ. “This cup,” said Jesus, in the usual version, “is the new covenant in my blood.” We have translated it slightly differently, “This cup is the new covenant and it cost my blood.” The Greek preposition en most commonly means in; but it can, and regularly does mean at the cost or price of, especially when it translates the Hebrew preposition be. Not a covenant is a relationship entered into between two people. There was an old covenant between God and man, an old relationship. That old relationship was a relationship based on law. In it God chose and approached the people of Israel and became in a special sense their God; but there was a condition, and the condition was that, if this relationship was going to last, the people of Israel must keep God’s law. (cp. Exodus 24:1-8). The continuance of the covenant depended on the keeping of the law. But with Jesus a new relationship is opened to man, and it is a relationship which is dependent not on law but on love. It depends not on man’s ability to keep the law—for no man can do that—but on the free grace of the love of God offered to men. This changes the whole relationship of God to man. Under the old covenant man could do nothing other than fear God for he was ever in default for he could never perfectly keep the law; under the new covenant man comes to God as a child to a father and not as a criminal to a judge. And—however you look at things—it cost the life of Jesus to make that new relationship possible. “The blood if the life,” says the law (Deuteronomy 12:23). It cost Jesus’ life, Jesus’ blood as the Jew would put it to make that relationship possible. And so the scarlet wine of the sacrament stands for the very life-blood of Christ without which the new covenant, the new relationship of man to God, could never have been possible. (pp. 115-16)
Problems with Some Popular Interpretations of 1 Cor 15:29 and “Baptism for the Dead”
(i) Beginning from the meaning of over or above, some scholars have suggested that this refers to those who got themselves baptized over the graves of the martyrs. The idea is that there would be something specially moving in being baptized on sacred ground with the thought of the unseen cloud of witnesses all around. It is an attractive and rather a lovely idea, but, at the time Paul was writing to the Corinthians, persecution had not yet broken out in anything like a big way. Christians might suffer ostracism and social persecution, but at the time of the martyrs had not yet come.
(ii) It is in any event much more natural to take huper in the sense of instead of or on behalf of. If we take it that way there are three possibilities. It is suggested that the phrase refers to those who get themselves baptized in order to fill up the vacant places in the Church which the dead have left. Again it is a great thought. The idea is that the new believer, the young Christian, comes into the Church like a new recruit to take the place of the veterans who have served their campaign and earned their release. There is a precious thought here. The Church ever needs its reinforcements, its replacements, and the new member of the Church is like a new volunteer who fills up the depleted ranks.
(iii) It is suggested that the phrase means those who get themselves baptized out of respect for and affection for the dead. Again there is a precious truth here. We know it to be true that many of us came into the Church because we knew and remembered that someone whom we had loved and who had loved us had died praying and hoping for us. There are many who have in the end given their lives to Christ because of the unseen influence of one who has passed over to the other side.
(iv) All these are lovely thoughts, but in the end we think that this phrase can only refer to one custom, a custom which existed in the early church . . . in the early church were was a custom of vicarious baptism. (pp. 170-71)