How does the Shi'ite view of Infallibility of the Prophets and the Imams reconcile with the examples in Qur'an?

As I understand, the subject of infallibility of the Prophets (peace be upon all of them) is dealt differently in Sunni and Shi'ite theology. I believe it is necessary to present my understanding of both views before I can ask the question. > **Sunni View** > > We believe that the Prophets are infallible with respect to all they > conveyed from Allah, in word, deed and what they approved of. The > majority of Sunni scholars also viewed that the prophets were > protected from major sins but not from minor sins. With regard to > minor sins, these might have been committed by them. However, if they > committed such actions, they were not left to persist, rather, Allah > (Exalted be He) pointed that out to them and they hastened to repent. > We can witness that in several ayah in Qur'an: > > The Story of Prophet Adam (عليه السلام): > > > ... And Adam disobeyed his Lord and erred. Then his Lord chose him and > > turned to him in forgiveness and guided [him]. **[\[Surah Taha 20:121-122\]][2] ** > > Or Prophet Musa (عليه السلام) also committed a mistake of killing an > Egyptian man. In Verse **28:16 ** of the Quran, Allah Almighty > says: > > > He said, "My Lord, indeed I have wronged myself, so forgive me," and > > He forgave him. Indeed, He is the Forgiving, the Merciful. > > And there are similar mention about Prophet Dawud (عليه السلام) > and in many Ayahs, Allah corrects Prophet Muhammad (صلّى الله عليه > وآله وسلّم) like in Surah At-Tahrim 66:1 or Surat 'Abasa or > Surah Al-Anfal . It is also worth mentioning the hadith of the > pollination of palm tree where the Prophet (صلّى الله عليه وآله > وسلّم) made a mistake in worldly affair. In my perspective (correct me if I am wrong), the following is the Shi'ite view regarding the Prophets (peace be upon all of them) and *also*, the Imams (including the twelve Imams). > **Shi'ite View:** > > - The Prophets and Imams are free and protected from *both* major and minor sins. > - The Imams are free from errors. > - The Imams do not make mistake with respect to worldly affairs. > - The Imams do not forget anything. How does the above presented ayah reconcile with the Shi'ite view?