Islam places great emphasis on each individual taking account of one's actions. Setting aside some time during the end of the day to evaluate ourselves and work on our weaknesses is highly commendable and is one of the best methods towards improving oneself. On the flip side of that, there are people who take it upon themselves to evaluate the faults in others instead of themselves. Maybe they cannot find any faults in their own actions, so they try to do accounting of the self for others as well. In any case, concerning ourselves with the faults of others is highly looked down upon in Islam. There are verses in the Qur'an which speak to this specifically and a large number of traditions from the books of Hadith that confirm this.
Now, there are sincere people who will let people know in private that they are going on the wrong path and try to guide them the best way possible. Imam Ali (peace be upon him) says concerning such sincere individuals, "Let the best person in your estimation be that person who points out to you your faults and shortcomings and presents them to you as a gift." Fault-finding as a sin does not apply to them as they are practicing Amr Bil Ma'ruf and Nahi Anil Munkar in the correct way.
Occupying oneself with finding fault in others can lead to many evils. Islam teaches us to overlook the sins and mistakes of others, just as God overlooks our sins and mistakes and doesn't make them public. On the first level, just seeing or knowing someone committed a sin is not enough to accuse them. You can see a brother walk into a bar and assume he went in to have an alcoholic drink, when in reality he could have just needed to get some water to take some medicine with. We are not all-knowing, and should not pretend to be. Imam Ali has said, "Accept the apology of your Muslim brother, and if he has not any, invent one for him yourself." If there could be a reasonable explanation why someone apparently did a sin or made a mistake, we should accept it and move on. This is one reason why finding fault in others is a dangerous action.
In verse 11 of Sura Hujarat, God says, "O you who believe, let not (one) people laugh at (another) people perchance they may be better than they, nor let women (laugh) at (other) women, perchance they may be better than they; and do not find fault with your own people nor call one another by nicknames; evil is a bad name after faith, and whoever does not turn, these it is that are the unjust." This verse brings to light one of the other reasons why finding fault in others is a terrible act, which is that it can lead to animosity and humiliation for people in the community. Those who do such an action are called unjust by God, and rightfully so. This action can tear apart a community in a very short period of time. Imam Muhammad al-Baqir (peace be upon him) has said, "It is compulsory for every Muslim to conceal even seventy great faults of his fellow Muslims (in order to save his prestige)." He has also said, "The worst form of betrayal is the disclosure of confidential information." Hurting the reputation of a fellow Muslim is a grievous act, because sometimes it can be the only thing a person has. Allah could have made it easy for others to know our true reality, but he has hidden our sins and flaws from others. Maintaining the good reputation of our fellow Muslims is essential for the community, as it helps maintain mutual respect and allows the community move forward.
Finally, a big reason for not prying into others faults is that it takes away from one's own self-improvement and can in fact take one's soul even lower. There are many narrations that attest to this. Imam al-Baqir has said, "Sufficient is a person's own defect (in himself) that he tries to pick and look for faults in other people, when he himself has those same faults in himself (and does not recognize them)!" Imam Ali has also said, "One who contemplates his own flaws is too busy to consider other people's faults, and the one who is satisfied with whatever sustenance Allah has provided him does not grieve over that which he has lost. The one who observes the shortcomings of others, disapproves of them, and then adopts them for himself is truly a fool." These words of the Infallibles are enough of a warning against finding fault with others.
Those insincere people who find fault with others without looking at their own are truly a poisonous element in society. Not only do they corrupt their own soul, but they sow the seeds of animosity within the community and cause public humiliation and embarrassment. We should of course make sure that we do not have such a shortcoming in us, but we should also try to stay away and not give credence to these types of people in our communities.