"Let nothing be done through strife or vainglory; but in lowliness of mind let each esteem other better than themselves. Look not every man on his own things, but every man also on the things of others." (Phil 2:3-4)
Don't do anything out of selfish ambition or vain conceit, rather in humility, value others above yourself. Everyone should look out for their own interests as well as the interest of others.
What this comes down to is brotherly love. The "do unto others" theme rings true here, as it does in so many other areas. If you experience God's compassion, be compassionate to others. If you experience God's grace, be gracious to others. If you experience God's blessings, be a blessing to others. It's not really a difficult feat.
Far too often we are very aware of the faults of those around us, and we are quick to point them out. We need to be more aware of our own faults, working to rectify them in accordance with God's Word and the teachings of Jesus Christ. Only then will we be able to look past the faults of others and see the whole person, not just their faults. And yes, there are people who do not take the same inventory of themselves, but that is not for us to judge - there has to be a little "good" in each person we meet or interact with.
Take the time to examine yourself. Does what you do reflect a selfish or conceited nature or are you doing it humbly? Do you have a respect for others? Do you look out for others just as you look out for yourself? Inner peace can only truly be enjoyed when you have an unpretentious mind!