Hadith 1:

حَدَّثَنا عَبْد الواحِدِ بْنِ مُحَمَّدِ بْنِ عَبْدُوسٍ النِيْسابُوري العَطَّار رَضِىَ اللهُ عَنْهُ قالَ: حَدَّثَنامُحَمَّدِ بْنِ قُتَيْبَةَ النِيْسابُوري، عَن حَمْدانَ بْنِ سُلَيْمان، عَن عَبْد السَّلامُ بْنِ صالِح الهَرَوِيِ‏سَمِعْتُ أَبَا الحَسَن عَلِىِّ بْنِ مُوسَى الرِّضا عَلَيْهِ السَّلامُ يَقُولُ رَحِمَ اللَّهُ عَبْداً أَحْيَا أَمْرَنَا فَقُلْتُ لَهُ وَكَيْفَ يُحْيِي أَمْرَكُمْ قَالَ يَتَعَلَّمُ عُلُومَنَا وَيُعَلِّمُهَا النَّاسَ فَإِنَّ النَّاسَ لَوْ عَلِمُوا مَحَاسِنَ كَلامِنَا لاتَّبَعُونَا

Narrated through a chain of trustworthy narrators that Imam Ali ibn Musa al-Rida (عليه السلام) said,

"May Allah have Mercy upon anyone who revives Our affairs (amr)."

I (the narrator) asked the Imam, "How can one revive Your affairs?" 

The Imam (عليه السلام) said, "He learns Our knowledge and teach it to the people. If the people come to know of the beauty of Our sayings, they would follow Us."

(partial hadith quoted here)

[Source: Ma’ani al-Akhbar, Shaikh Sadooq, Pg. 180]

Hadith 2:

أَحْمَدُ بْنُ مُحَمَّدِ بْنِ عِيسَى وَ مُحَمَّدُ بْنُ الْحُسَيْنِ بْنِ أَبِي الْخَطَّابِ وَ غَيْرُهُمَا، عَنْ أَحْمَدَ بْنِ مُحَمَّدِ بْنِ أَبِي نَصْرٍ، عَنْ كَرَّامٍ عَبْدِ الْكَرِيمِ بْنِ عَمْرٍو ، عَنْ‌ أَبِي بَصِيرٍ قَالَ: قُلْتُ لِأَبِي عَبْدِ اللَّهِ ع رَجُلٌ بَلَغَهُ عَنْكُمْ أَمْرٌ بَاطِلٌ فَدَانَ بِهِ فَمَاتَ، فَقَالَ: «يَجْعَلُ اللَّهُ لَهُ يَا أَبَا بَصِيرٍ مَخْرَجاً»، قُلْتُ: فَإِنَّهُ مَاتَ عَلَى ذَلِكَ، فَقَالَ: «لَا يَمُوتُ حَتَّى يَجْعَلَ اللَّهُ لَهُ مَخْرَجاً»

Narrated from Abu Basir who said, “I said to Abu Abdullah Imam al-Sadiq (عليه السلام), "A man to whom something (hadith) reached from you which was false/invalid* (batil), and he believed it, and then he died."

The Imam (عليه السلام) said, "O Abu Basir, Allah will provide him a way out of it"

Abu Basir said, "But he died on that (false) belief."

The Imam (عليه السلام) said, "He will not die until Allah provides him with a way out."

[Source: Mukhtasar al-Basari, Pg. 275-276]

Note: 

*False (Batil) here could mean due to Taqayyah or some other reason or due to misunderstanding of the meaning of the hadith.

This hadith indicates absolution of responsibility for those who took religion from the sayings of the Imams and achieving salvation through them, even if what reached him from the Imams was not actually correct due to being said under Taqayyah or some other reason, as Allah will provide him a way out of it.

Hadith 3:

 حُمَيْدُ بْنُ زِيَادٍ عَنِ الْحَسَنِ بْنِ مُحَمَّدٍ عَنْ وُهَيْبِ بْنِ حَفْصٍ عَنْ أَبِي بَصِيرٍ قَالَ سَمِعْتُ أَبَا عَبْدِ اللَّهِ (عليه السلام) يَقُولُ رَحِمَ اللَّهُ عَبْداً حَبَّبَنَا إِلَى النَّاسِ وَ لَمْ يُبَغِّضْنَا إِلَيْهِمْ أَمَا وَ اللَّهِ لَوْ يَرْوُونَ مَحَاسِنَ كَلَامِنَا لَكَانُوا بِهِ أَعَزَّ وَ مَا اسْتَطَاعَ أَحَدٌ أَنْ يَتَعَلَّقَ عَلَيْهِمْ بِشَيْ‏ءٍ وَ لَكِنْ أَحَدُهُمْ يَسْمَعُ الْكَلِمَةَ فَيَحُطُّ إِلَيْهَا عَشْراً

 Narrated through a chain of reliable narrators that Abu Abd-Allah Imam Sadiq (عليه السلام) said,

"May Allah have mercy on a man who makes Us lovable to the people and does not make Us hateful to them. By Allah that if they (i.e. the Shia) were to narrate Our beautiful speech (as is without any reduction/addition/modification) they would become honored by it, and no one would be able to criticize them for anything, but one of them hears a single statement and adds in it ten (of his own words/thoughts)."

[Source: al-Kafi, Vol. 8, Pg. 229, Hadith. 293]

*Allamah Majlisi comments on the last part of the hadith saying:

قوله عليه‌السلام: « فيحط إليها » أي ينزل عليها ويضم بعضها معها عشرا من عند نفسه فيفسد كلامنا ويصير ذلك سببا لإضرار الناس لهم

As for the saying of the Imam 'he adds in it' meaning he adds ten of his own (words) to the hadith, which corrupts Our speech and becomes a reason for people to harm them.

[Source: Mirat al-Uqul, Vol. 26, Pg. 163]