In The Name of Allaah, The Most Merciful, The Bestower of Mercy
Allaah [The Mighty and Majestic] said:
وَٱلَّذِينَ لَا يَشۡهَدُونَ ٱلزُّورَ وَإِذَا مَرُّواْ بِٱللَّغۡوِ مَرُّواْ ڪِرَامً۬ا
And those who do not witness Az-zoor [falsehood], and if they pass by some evil play or evil talk, they pass by it with dignity. [Surah Al-Furqaan. Aayah 72]
[ وَٱلَّذِينَ لَا يَشۡهَدُونَ ٱلزُّورَ- And those who do not witness Az-zoor (falsehood)]: Imaam Ash-Shawkaanee [rahimahullaah] said: They do not give witness to false testimony or attend gatherings of falsehood. Az-Zoor means lies and falsehood, and they do not bear witness to it. The second meaning held by the majority of the Mufassiroon is that Az-zoor in this Aayah means shirk and there is no lie greater than shirk. [Ref 1]
Imaam Ibnul Jawzi [rahimahullaah] quoted several different meanings of the term Az-zoor that it means: The idols of the idolaters, music, shirk, the past time or jest that used to take place during the era of pre-Islamic ignorance, lies, false testimony, the festivals of the polytheists and vulgar speech. [Ref 2]
Imaam As-Sadi [rahimahullaah] said: They keep away from all gatherings of unlawful deeds and speech, such as gathering where the Aayaat of Allaah are given false interpretations [or mocked at]. They keep away from false argumentation, impermissible backbiting [ref a], tale carrying, verbal abuse, false accusation, mockery, [places where alcohol] is consumed, picture making [of living things] etc; therefore, what is even more obligated is that they neither speak about these things [i.e. except with condemnation] nor participate in such activities. [Ref 3]
Qataadah [rahimahullaah] said: ‘’They do not help the people of falsehood in their falsehood.’’ [Ref 4]
[وَإِذَا مَرُّواْ بِٱللَّغۡوِ مَرُّواْ ڪِرَامً۬ا- and if they pass by some Laghw (evil play or evil talk), they pass by it with dignity]: Laghw – meaning acts of disobedience, the harm of the polytheists directed against them, falsehood, shirk, the mention of sexual intercourse and private parts [i.e. without a legislated Islamic reason for its discussion] etc.. they do past it with forbearance and turn away from it.[Ref 5]
They either say- in their hearts or by way of speech- to the perpetrators of such deeds: ‘’Your deeds are [attributed] to you and ours are [attributed] to us.’’ [Ref 6]
Regarding the Statement of Qataadah, ‘’They either say- in their hearts or by way of speech- to the perpetrators, ‘Your deeds are [attributed] to you and ours are [attributed] to us’’’, we remind ourselves of Allaah’s statement: [يَا أَيُّهَا الَّذِينَ آمَنُوا عَلَيْكُمْ أَنْفُسَكُمْ ۖ لَا يَضُرُّكُمْ مَنْ ضَلَّ إِذَا اهْتَدَيْتُمْ ۚ إِلَى اللَّهِ مَرْجِعُكُمْ جَمِيعًا فَيُنَبِّئُكُمْ بِمَا كُنْتُمْ تَعْمَلُونَ – O you who believe! Take care of your own selves. If you follow the right guidance no hurt can come to you from those who are in error. The return of you all is to Allah, then He will inform you about (all) that which you used to do]. [Surah Al-Maa’idah. Aayah 105]
Allaah [The Most High] said: يَا أَيُّهَا الَّذِينَ آمَنُوا عَلَيْكُمْ أَنْفُسَكُمْ ۖ O you who believe! Take care of your own selves]- Meaning: Strive in rectifying and perfecting your own souls and keep them firm upon the straight path; because if you are righteous, you will not be harmed by the one deviated from the straight path and is not guided to the upright religion; rather he only harms himself. [However], this does not indicate that the slave [i.e. the Muslim] is not harmed if he abandons enjoining good and forbidding evil and is negligent towards it; for indeed his guidance will not be complete except through fulfilling what is obligated on him in relation to enjoining good and forbidding evil. Yes, if he is [genuinely] unable to stop evil with his hand and his tongue, but rejects it in his heart, then indeed he will not be harmed by the misguidance of others.
[إِلَى اللَّهِ مَرْجِعُكُمْ جَمِيعًا -The return of you all is to Allah]- Meaning: Your final destination is the day of Judgement and your gathering will be in the presence of Allaah [The Most High]; [فَيُنَبِّئُكُمْ بِمَا كُنْتُمْ تَعْمَلُونَ – then He will inform you about (all) that which you used to do]- Meaning:[your] good and evil [deeds].[Ref 7] [End of quote]
Question to Imaam Abdul Azeez Bin Baaz (Rahimahullaah):
Is enjoining Good and Forbidding Evil obligated on all Muslims or is it just confined to those in authority and their deputies?
Correcting what is wrong is obligated on all Muslims according to their ability, because the Messenger [sallal laahu-alayhi-wasallam] said, ‘’Whoever sees an evil [i.e. that which is unlawful in Islamic law], then let them stop it with their hand [i.e. by taking action]; but if not able, then with his tongue [by speaking]; and if able, then with his heart [i.e. by hating it], and that is the weakest of Eemaan.’’ [Reported by Imaams Muslim, Abu Dawood, Tirmidhi & others]
However, stopping evil by the hand must be based on ability and not result in greater corruption or evil. A man has the right to rectify matters with his hand [by taking action] in his home; a manager has the authority to stop something with the hand within the organization he is responsible for- in accordance with the instructions he has been given [i.e. authority given to him by the state or recognised government]; otherwise, people should not stop evil- with their hand- which they are not authorised to stop. If they do so, this will result in more evil and great corruption between them and the people, and between the people and the state. In this case they should make the change with their tongue [i.e. by speaking]. They may say: “O such and such! Fear Allah! This is not permissible,” “This is Haram,” or “This obligated on you,” and clarify it through a legislated Islamic proof. [NB: In the UK, objecting to certain behaviour can be viewed as harassment or verbal abuse, therefore a Muslim should be aware of what the law allows him before he says or does anything whilst living in the West].
As for changing matters with the hand, this should be done where one has authority, such as one’s home [i.e. within what the law allows] in relation to those under one’s responsibility, or those authorized by the ruler, such as organizations given permission and authority to enjoin good. They should make changes in accordance with the authority given to them- in a manner legislated by the Islamic law and without exceeding their jurisdiction. The same applies to the governor of a city; he should make changes with his hand- in accordance with the instructions he has been given.
[Ref 1]: Fat-hul Qadeer’ Vol 4. page119. Daarul Wafaa. 1st Edition 1435AH 
[Ref 2:] Zaadul Maseer Fee Ilmit Tafseer. Slightly paraphrased
[Ref 3]: Tafseer As-Sadi. Slightly paraphrased
[Ref 4]: Fat-hul Qadeer’ Vol 4. page119. Daarul Wafaa. 1st Edition 1435AH 
[Ref 5] Zaadul Maseer Fee Ilmit Tafseer. Slightly paraphrased
[Ref 6]: Badaa’i at-Tafseer Al-Jaami Limaa Fassarahu Al-Imaam Ibnul Qayyim 2/271
[Ref 7] Tafseer As-Sa’di. Slightly paraphrased
[Ref 8]: An Excerpt from Fataawa Ibn Baaz 8/208. Slightly paraphrased