In his sermon Gospel Enemy #1: Self-righteousness, Jerry Bridges has the following to say on what it does to a person:
Self-righteousness causes you to trust in yourself, like the Pharisee in Luke 18:9-14. He trusted in his observance of the law to set him right with God.
Self-righteousness causes you to look down on others. The Pharisee in the parable above despised the tax collector. Similarly, Christians today may look down on homosexuals and other flagrant sinners.
Self-righteousness can make you feel God is unfair to you, for example when you expect something from God in reward for obedience, like the older brother in Luke 15:25-30.
Self-righteousness blinds you to how much you’ve been forgiven. The self-righteous person doesn’t sense any need for forgiveness, like Simon the Pharisee in Luke 7:36-47. As a consequence, the self-righteous person loves little.
The cure for self-righteousness is to realize how much we’ve been forgiven. Instead of comparing ourselves with others, like the tax collector, we compare ourselves with God saying, “God, be merciful to me, a sinner.”
When we love much because we’ve been forgiven much, we’ll want to obey much. Not to earn favour, but because we have it. When we love much because we’ve been forgiven much, we’ll serve much—in sacrificial obedience to God.
You can also listen to the entire sermon (length—40:10).