If the motive is, like you say, to let someone have it, then the confrontation is no longer correction done in love but instead the type of judgment that actually is warned about. Most likely such a confrontation will not reap repentance since the plank has been ignored while the speck is attacked.

People, even Christians, like using "the bible says judge not, lest ye be judged", to support their opposition to anyone confronting them about sin. In reality, the bible supports certain judgments. We are to confront people in a loving, gentle way. When someone sins against us we are to show them their fault (Matt. 18:15). We are not to condemn but we are to correct. If my motive when approaching you is to 'let you have it' then my motives are not pure. If my motive is to see you free from your sin so you can better serve Christ as well as restore my relationship with you then I'm showing a pure motive. Correct judgment is more about you than me. It's me caring more about your sanctification than my vindication.