‘For first of all’ – this is not the only case in which Paul does this: he introduces his first point, and never tells us what the second point is; and we are left to figure it out for ourselves. The second point is probably what begins in chapter 12, ‘Now, concerning spiritual gifts’.
What does this phrase ‘I partly believe it’ mean? Did he or didn’t he believe it? It possibly means something like this – that the people who have reported on the sad state of affairs in Corinth have been so scandalised by it, they have tended to overstate it; and the apostle means, ‘I do not necessarily think it is exactly as described to me, but the reports certainly are credible and something is wrong. I partly believe it. So it is important to address this.’