Are there examples of ijtihad by Ali ibn Abi Talib and the Companions in general (may Allah be pleased with them all) that led to their contravention of the authentic, established Sunnah, along with an explanation and commentary on them?

The Companions are not infallible, and they may err. Therefore, they were commanded to refer to the Qur’an and Sunnah (definition) in case of dispute, as Allah Almighty says: (And if you disagree over anything, refer it to Allah and the Messenger).

The error of a Companion does not diminish his status, and he has legitimate excuses, such as the Sunnah not reaching him, or his ijtihad (definition) (independent reasoning) in understanding it. An example of the former is Ali’s burning of the apostates, in which he contravened the Prophet’s prohibition of torture by fire because he was unaware of the prohibition. An example of the latter is Uthman and Aisha completing the prayer during travel, interpreting it to mean that shortening is a concession and that completing the prayer is better for those who do not find it difficult, whereas shortening is an emphasized Sunnah.