Islam has a similar concept called 'Ismah, which denotes a divinely-ordained freedom from error (in religious matters). Who does (or does not) possess 'ismah is a point of contention between the major sects.
While the Qur'an itself does command followers to "obey Allah and obey the Messenger and those in authority among you," Sunnis and Shi'ites disagree as to whether this automatically confers 'ismah to "those in authority." (or, vice-versa, whether this prevents those who don't possess 'ismah from becoming "those in authority.")
The Shi'a belief, based in part on the related revelation that "Allah does not order immorality," is that God's command to obey those in authority means that such obedience cannot possibly involve immorality. The Shi'a Imams are thus considered Infallible in much the same sense as the Catholic Pope is.
Sunnis, however, typically only consider the prophets themselves to have 'ismah, and interpret these ayat differently: The fact that God does not command immorality is treated as a limit to obedience; even if ordered to obey, it is not incumbent to follow a command that is known to involve disobedience to God. As such, some degree of questioning-of-authority is to be expected (and accepted), even though commands in matters that do not involve transgression are still to be obeyed.
(What does, or does not, qualify as "disobedience to God" thus can again be a point of contention.)
As for lesser forms of authority (e.g. as in the question, a son to his father), it is commonly believed by both Sunni and Shi'a that obedience is akin to the Sunni position above: It is only mandated when it does not otherwise involve sin.