Praise be to Allah.

Firstly: 

There is no contradiction between what is proven in sharee’ah, whether between one aayah and another, between one hadeeth and another, or between aayahs and ahaadeeth. All of it is Revelation (wahy) from Allaah. Allaah says (interpretation of the meaning): 

“Had it been from other than Allaah, they would surely, have found therein many a contradiction”

[al-Nisa’ 4:82]

If there appears to be a contradiction, that is in our own minds and because of our misunderstanding, not in the texts themselves. Hence the scholars took the care to explain the texts in which there may appear to be a contradiction and to dispel any confusion that may have arisen in some people’s minds concerning some texts. With regard to the question, there is no contradiction – praise be to Allaah – between the words of the Prophet (peace and blessings of Allaah be upon him), “Whoever among you sees an evil action, let him change it with his hand [by taking action]; if he cannot, then with his tongue [by speaking out]; and if he cannot, then with his heart [by hating it and feeling that it is wrong] – and that is the weakest of faith” (Narrated by Muslim, 49), and his words, “Part of a person’s being a good Muslim is his leaving alone that which does not concern him” (narrated by al-Tirmidhi, 2317, classed as saheeh by Ibn al-Qayyim in al-Jawaab al-Kaafi, p. 112) 

It is not possible under any circumstances that Islam would oblige the person who sees an evil action to change it, then at the same time tell him that it is better not to denounce it. 

The circumstances in which the first hadeeth applies are different from those in which the second hadeeth applies.  

This is similar to what some people understood from the verse (interpretation of the meaning): 

“O you who believe! Take care of your ownselves. If you follow the (right) guidance [and enjoin what is right (Islamic Monotheism and all that Islam orders one to do) and forbid what is wrong (polytheism, disbelief and all that Islam has forbidden)] no hurt can come to you from those who are in error”
[al-Maa’idah 5:105]

But Abu Bakr al-Siddeeq (may Allaah be pleased with him) guided them to the correct understanding, and the scholars (may Allaah have mercy on them) explained that. 

It was narrated that Abu Bakr al-Siddeeq (may Allaah be pleased with him) said: “O people, you recite this verse (interpretation of the meaning): 

‘O you who believe! Take care of your ownselves. If you follow the (right) guidance [and enjoin what is right (Islamic Monotheism and all that Islam orders one to do) and forbid what is wrong (polytheism, disbelief and all that Islam has forbidden)] no hurt can come to you from those who are in error’
[al-Maa’idah 5:105]

I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say, ‘When the people see an oppressor but they do not try to stop him, soon Allaah will cause all of them to suffer punishment because of him.’”  

(Narrated by al-Tirmidhi, 2168; Abu Dawood, 4338; Ibn Maajah, 4005). 

This hadeeth was classed as saheeh by al-Tirmidhi and Ibn Hibbaan, 1/540. 

Shaykh al-Islam said concerning what we learn from the verse “Take care of your ownselves…”: 

“… Enjoining what is good and forbidding what is evil in the manner prescribed in Islam, based on knowledge, kindness, patience, good intentions and doing it in the proper manner, is included in the phrase “Take care of your ownselves…” and in the phrase “If you follow the (right) guidance”. 

These five things are what may be learned from the aayah, for the one who is commanded to enjoin what is good and forbid what is evil. 

There is also another meaning which is that a person should focus on his own interests by seeking knowledge and acting upon it, and not worry about that which does not concern him, as the Prophet (peace and blessings of Allaah be upon him) said: “Part of a person’s being a good Muslim is his leaving alone that which does not concern him.” Especially being too curious about that of which a person has no need to know about another person’s religious commitment or worldly affairs, and especially if he is speaking because of hasad (destructive envy) or competing in leadership.  

Majmoo’ al-Fataawa, 14/482 

And he (may Allaah have mercy on him) said: 

The believer has to fear Allaah with regard to His slaves and it is not his responsibility to guide them. This is the meaning of the verse (interpretation of the meaning): 

‘O you who believe! Take care of your ownselves. If you follow the (right) guidance [and enjoin what is right (Islamic Monotheism and all that Islam orders one to do) and forbid what is wrong (polytheism, disbelief and all that Islam has forbidden)] no hurt can come to you from those who are in error’
[al-Maa’idah 5:105]

Calling others to guidance means doing what is obligatory. If the Muslim does his duty of enjoining what is good and forbidding what is evil, and does his other duties as well, then the misguidance of those who have gone astray will not harm him. That may be achieved sometimes by the heart, sometimes by the tongue and sometimes by the hand. In the case of the heart, this is obligatory in all circumstances because doing it will not cause any harm. Whoever does not even do that is not a believer, as the Prophet (peace and blessings of Allaah be upon him) said, ‘And that is the weakest of faith.’”  

(Majmoo’ al-Fataawa, 28/126-128) 

So it is known that denouncing evil is one of the things that concern the Muslim, and he must denounce it as much as he is able and in accordance with the interests of sharee’ah. That which does not concern him cannot be something that is waajib (obligatory) or mustahabb (encouraged).  

There follow the comments of the scholars on the interpretation of the hadeeth, “Part of a person’s being a good Muslim is his leaving alone that which does not concern him.” 

(a)Shaykh al-Islam Ibn Taymiyah said:

The Muslim is commanded either to speak good or to keep silent. If he turns away from the silence that is enjoined upon him and speaks in a unnecessary manner that is not good, then this is counted against him. Hence the Prophet (peace and blessings of Allaah be upon him) said: “Part of a person’s being a good Muslim is his leaving alone that which does not concern him.” If a person indulges in something that does not concern him, that detracts from his being a good Muslim. 

Majmoo’ al-Fataawa, 7/49, 50 

(b)Ibn al-Qayyim (may Allaah have mercy on him) said:

The Prophet (peace and blessings of Allaah be upon him) summed up all of piety in one sentence, when he said: “Part of a person’s being a good Muslim is his leaving alone that which does not concern him.” This includes not speaking about, looking at, listening to, striking a blow, walking towards or thinking about anything for no purpose, and keeping away from all outward and inward actions that have to do with things that do not concern you. This sentence is sufficient concerning piety. 

(c)Ibraaheem ibn Adham said:

Piety means leaving alone all doubtful things and leaving alone that which does not concern you means leaving alone all that is superfluous. 

In al-Tirmidhi there is a marfoo’ report according to which the Prophet (peace and blessings of Allaah be upon him) said: “O Abu Hurayrah, be pious and you will be the most devoted of people (to Allaah).”  

Madaarij al-Saalikeen, 2/21 

(d)Ibn Rajab al-Hanbali said:

This means giving up haraam things, doubtful things, makrooh things, and excessive permissible things that are unnecessary, because all of these things do not concern the Muslim if his Islam is perfect and he has attained the level of ihsaan. The most important aspect of leaving alone that which does not concern you is guarding your tongue against idle speech. 

Jaami’ al-‘Uloom wa’l-Hukam, 1/309-310 

(e)al-Zarqaani said:

Some of them said that what comes under the heading of leaving alone that which does not concern you is learning branches of knowledge that are not important and ignoring those that are more important, such as one who neglects to acquire knowledge that is in his own interests and occupies himself with learning something that does not benefit anyone else, such as philosophical debate, and says as an excuse, ‘My intention is to benefit people.’ If he were sincere he would have started by learning the type of knowledge that would help him to be guided and cleanse himself of all blameworthy characteristics such as destructive envy (hasad), showing off, arrogance, self-admiration, rivalry with one's peers, trying to put people down and other characteristics and actions that may doom a person to Hell. 

Ibn ‘Abd al-Barr said: this hadeeth is an example of concise speech which includes many noble meanings in a few words, and it is one of the things that were said by no one before him. 

Sharh al-Zarqaani, 4/317 

(f)al-Mubaarakfoori said:

Al-Qaari said – concerning the meaning of leaving alone that which does not concern him – this means that which is not his business and which it does not befit him to say, do, look at or think about. And he said: what is meant by that which does not concern him is that which he has no need of and is not essential to his spiritual or worldly affairs, and will not help him to earn the pleasure of his Lord, because he is able to live without it, and he can put his affairs straight without it. This includes all superfluous deeds and words. 

Tuhfat al-Ahwadhi, 6/500 

Secondly: 

With regard to what is to be denounced: this includes every reprehensible action which Islam stated is abhorrent and which leads to bad consequences for the one who does it, such as zina (adultery), riba (usury, interest), looking at haraam things, listening to haraam things, shaving the beard, allowing one's garment to hang below the ankles, severing the ties of kinship, introducing innovations into the religion, and so on. 

It is not necessary to be in a position of authority in order to change evil actions by one's hand, or to be a scholar in order to change them by one's tongue, rather it is sufficient to be able to change them provided that that does not result in a greater evil than the one that you are denouncing. It is sufficient for you to know that this is evil according to sharee’ah, so you denounce it by speaking out. 

With regard to changing evil actions by one's heart. This means hating this evil thing in your heart and leaving the place where it is happening. 

With regard to your question about seeing some evil things and wondering whether you should denounce the people who are doing them or inform the authorities, our answer is that it depends on the action in question and on who is doing it. If you see an evil action on the part of someone that you cannot leave him and go and tell the authorities about it, then you have to denounce him straightaway, because it may be too late otherwise. 

But if the evil action is major and serious, and you cannot denounce it on your own, then you have to inform the authorities. 

The point is that evil must be removed, whether by your hand or the hand of someone else. If that is not possible then it must be done by your tongue (by your speaking out), and you should not worry whether they listen to you or turn away from you; all you have to do is convey the message. Allaah may sow the seeds of guidance in the heart of one of them because of your words, but the Shaytaan may also suggest to you that you should forget about denouncing them on the basis that they will not listen to you – so beware of that.

 And Allaah knows best.