Did Adam commit a sin? What about the question of the infallibility of the divinely sent prophets?

In order to arrive at the answer, a few preliminary points must be considered. It must first be pointed out that the Divine prophets and their deputies enjoy lofty spiritual and existential stations in the order of existence. They are the hidden rays of Divine effusion; the complete manifestations and clear signs of the Beauty and Majesty of the Truth. The clay of their bodies and the forms of their souls were moulded by the might of both of the Divine arms-Beauty and Majesty-and were taught the reality of the Divine Names and Attributes in the pre-eternal world of the Unseen.

The second point that must be addressed is in regard to the question of infallibility. There are a range of views in this regard, among them:
1. They are infallible vis-à-vis the major sins but are vulnerable to the minor sins;
2. They are vulnerable to both major and minor sins;
3. They do not commit sins intentionally but may do so by mistake;
4. They are absolutely infallible.
The final view, which is the correct one, is that of the Shi’a and is supported by a variety of reasons, one of which is that if they were vulnerable to sin, it would defy the purpose of their mission, for in that case the masses would not be willing to trust and follow them; such a scenario runs contrary to the wisdom of the Omniscient Lord.

Now the cause of their infallibility is their all-encompassing knowledge of obedience and disobedience, of what is permitted and what is forbidden, and generally speaking of vice and virtue (or in a word, their theoretical intellect) that keeps them from sinning (which is carried out by the faculty of the practical intellect).
A relevant question in the context of Adam’s (a.s) sin is where Adam (a.s) resided before banishment. It could not have been the promised Paradise; for, firstly, as asserted in the Divine Text leaving Paradise is not possible; secondly, Satan is not allowed in Paradise, and finally, there are no restrictions on the consumption of any fruit in Paradise.
The last point meriting mention in this context is in regard to the nature of Adam’s (a.s) error. One of the posited explanations is that it was not a sin but a neglect of what was more meritorious (tark awla); for, firstly, prophets are infallible; secondly, considering the lofty station of the prophets, it would not be inappropriate for them to be upbraided on account of neglecting what is more meritorious-hence, the adage, “The righteous deeds of the good folk are the sins of those brought nigh to Him;” thirdly, neglecting the more meritorious has in fact occurred among the prophets-as in the story of Yunus (a.s)-and so is a likely possibility.
But as to the question of why Adam and Eve (a.s) were not forbidden from the consumption of the forbidden fruit on earth as they were in the Garden of Eden, there are several possible explanations. It is possible that the forbidden tree was an actual tree, a plant, the consumption of which entailed banishment from the heavenly life that they were enjoying, and as such there would have been no reason for the prohibition of that tree on earth. And as elucidated in the appropriate place, religious directives vary based on location, time, and other particular circumstances.
Another possibility is that the tree in question was a spiritual reality. In this case, that tree was either the tree of knowledge, which is of course not defensible as it is contradictory to definitive Qur`anic and traditional principles. For, as related in the Qur`an, Adam (a.s) was not only not restricted in the acquisition of knowledge but in fact he was taught all the “names” thus becoming the teacher of the angels.
Another possibility is that the tree is a metaphorical allusion to the trait of envy. Of course since Adam (a.s) was a messenger of God, the envy in question should be construed as a sort of longing, possibly a longing for the spiritual station of the Prophet of Islam, ‘Ali, Fatima, Hasan, and Husayn (a.s). Also in this context it may refer to the condemnation of jealousy before entering this world.