FIRST CORINTHIANS: 
Reported to Paul (1:11; 5:1)
Divisions/Boasting/Evaluating Leaders
Associating with the “Immoral”
Lawsuits
“All Things are Lawful” (6:12; 10:23)
Things “Concerning which” they wrote (7:1; 8:1; 12:1)
Marriage?
Food offered to idols? temples, marketplace, dinners
[Might 9:1-10:22 be interpolated from another letter?]
Evaluation and use of “spiritual gifts”
Other Matters— Likely Reported (Chaps. 11 & 15)
Women covering their heads
Divisions at the Lord’s Supper
Some denying the resurrection of the dead
SECOND CORINTHIANS:
(fragmented, possible reconstruction of several letters and pieces of letters)
10:1-13:14 Heated dispute with “false apostles;” strong opposition to Paul.
2:14-6:13; 7:2-4 Jewish Christian criticism of Paul’s ministry, his defense. These opponents seem different from those reflected in Galatians and also in 1st Corinthians. They have likely arrived recently in Corinth and introduced a new set of issues.
1:1-2:13; 7:5-16 Things seem resolved, tone of harmony prevails
Fragment 6:14-7:1 (possibly part of the “first” letter Paul wrote–the one he mentions in 1 Corinthians 5:9)
Chapters 8 & 9 on collection (cf. 1 Cor. 16:1ff) These seem to be floating without much context and also might be part of that missing “first” letter.
 

FIRST CORINTHIANS: 
ISSUES AND PROBLEMS IN MORE DETAIL
Divisions/jealousy, strife, criticism of leaders (1:10-4:21)
Man living with his stepmother (5:1-13)
Taking one another to court/lawsuits (6:1-8)
General (sexual) immorality/libertine attitude/prostitutes (6:9- 20)
Disputes about marriage, divorce, celibacy, changing states of life (slavery, circumcision) (7:1-40)
Eating meat sacrificed to idols/eating in idol temple (8:1-13; 10:1-33) [note difference in tone in 10:1-22]
Rights of Paul to take financial support as an apostle–his defense of his ministry against sharp criticism (9:1-27)
Disputes over women’s hair length/style (“veils”) (11:1-16)
Greed and drunkenness at the “Lord’s Supper” (11:17-34)
Pride/divisions over “spiritual gifts;” confusion in the assembly (chaps 12-14)
Some in community were denying the resurrection (15:1-58)