First, the text and then some comments.

The spiritual man makes judgments about all things, but he himself is not subject to any man's judgment: "For who has known the mind of the Lord that he may instruct him?" But we have the mind of Christ. (NIV)

• When Paul says that the spiritual man makes judgments about all things it is in contrast to the worldly man who can only judge worldly matters with human wisdom. It does not mean that the spiritual man's judgement is perfect as we will see in chapter 4. The Corinthians (as worldly people) are trying to judge Paul in spiritual matters.
• To make the interpretation of the second part of verse 15 clear, the NKJV adds the word “rightly.” The spiritual man will be judged by men using human wisdom. It just will not often be the right judgement. Certainly Gideon was crazy to attack the Midianites with such a small army...from a worldly perspective.
• Paul finishes his explanation of why the Corinthians are not qualified to judge him (and other leaders) by noting how far God is beyond man and that God's wisdom has been revealed to Paul. I tend to think that Paul uses “we” in this verse to refer to himself and the other teachers — not to say that it cannot be applied to mature believers in general.