1 Corinthians 4:1-5

Paul doesn't care at all about any sort of human judgement (v3). This includes his own judgement, so he doesn't even judge himself (v3). Clearly what matters is the fact that Paul states: "It is the Lord who judges me." (v4, ESV). With this in mind, Paul presents an application, "Therefore, do not pronounce judgement before the time, before the Lord comes," (v5, ESV). From this we should stop judging one another. From the bible it seems to teach us to judge and not to judge. First that comes to mind is this:

Do not judge, or you too will be judged.

(Matthew 7:1, NIV)

But even looking to the next chapter in 1 Corinthians we find this verse:

For what have I to do with judging outsiders? Is it not those inside the church whom you are to judge?

(1 Cor 5:12, ESV)

So we're taught to judge and not to judge. However, with reference to the verse in question, I think it is referring to motives. Do not judge other people's motives.

Therefore do not pronounce judgement before the time, before the Lord comes, who will bring to light the things now hidden in darkness and will disclose the purposes of the heart. Then each one will receive his commendation from God.

(v5, ESV)

This kind of judging is hidden because God will bring it to light. This leads me to believe this is a judgement on motives, because you can't tell what a person's motives are for sure. However, what you can judge are actions. In the case for 1 Corinthians 5 it is referring to a person who has his father's wife. What he has done is clearly a sin. It is not a question of motive, but it is an action that is clear for all to see.

So, do not judge other people's motives. God will bring it to light eventually, so it is not for us to bring to light.