See the section on judgment in this essay:
Three Secret Strategies of Satan
Here are a couple excerpts:
The kinds of judging we should do:
We are to judge the teaching of teachers, the opinions of people, the attitudes and behaviors of people. If we don’t, then we allow sin and Satan to exploit the weak and ignorant and vulnerable with his lies.
We are to preach the Truth and rebuke those who assert error—not in an attitude of rock throwing or some sort of controlling self-righteousness, but in a loving attitude of helping the person return to God (2 Timothy 4:2). We are our brothers’ keepers (ref., Mark 12:31; Luke 10:25-37; Matthew 7:12; 18:23-35; Luke 6:31). We have a responsibility to warn and admonish our brethren in the faith, just as we have a responsibility to our blood-brothers to warn them when they go astray because we love them.
St. Paul to the Romans exhorted good Catholics to instruct one another (Romans 15:14). To instruct someone necessarily means to evaluate (another word for judge) the one to whom instruction is given.
The Catechism of the Catholic Church states (No 1868): “… we have a responsibility for the sins committed by others when we cooperate in them: by (among several actions on our part) not disclosing or not hindering them when we have an obligation to do so.”
We cannot “disclose” a sin without first assessing (yet another word for judging) that the sin is in fact there in the first place.
In addition, one of the traditional seven Spiritual Works of Mercy is to “Admonish the sinner.”
Again, we cannot admonish that which we refuse to recognize in the sinner. We must make an assessment (judgment) that the person is sinning and thus “needs” admonishment.
The kinds of judging we shouldn’t do:
The most famous of the several “do not judge” passages are found at Matthew 7:1-3
*Judge not, that you be not judged. For with the judgement you pronounce you will be judged, and the measure you give will be the measure you get. Why do you see the speck that is in your brother’s eye, but do not notice the log that is in your own…" *
In this passage we see three kinds of judgment we are not to do:
Judgment of Condemnation: Judgment in this passage is referring to condemning (“pronouncing” judgment on a person’s soul). We are not the “Judge” to pronounce condemnation on anyone (not even ourselves). Only God can do that. The Church, for example, never pronounces “anyone” in hell. And even in the assessment of a person declared a saint, it is done by special dispensation granted to the Church by her authority of the “keys”. But even with this authority, we need to note that it is never applied to judging a person in hell. If the Church, who has the authority of the keys will not judge a person to condemnation, how can we? We are never to judge a person’s state of soul. Jesus tells us that we will receive ourselves the judgment of soul that we place on others if we attempt this usurpation of God’s sovereignty.
Judgment from Double–Standards: When we use double–standards for judgment, apply one measure to others and a different measure to ourselves we commit a sin. Jesus says that we will not get by with that (a form of hypocrisy). The standards we apply to others will be applied to us as well.
Judgment from Self-Righteousness: The last sentence of the passage quoted refers to seeing sins in others but not in oneself. This is self-righteousness (another form of hypocrisy).