Well I could say, the probability of one doing an error increases in this fashion...
God < Prophets < Imams(Shias) < A person who sticks to Qur'an and abides by it < A normal believer < Non Believer < Satan.
Are certain authority figures "always right"?
Well God is of course, Errorless. The rest varies. Some say, prophets could be error less, while some say, prophets could've done minor negligible errors but aren't errorless. Some say, Imams (Shias) are infallible alongside the prophets, while some say, anyone could do mistakes. Again, this is solely opinion based as described in the above order.
Is it wrong to challenge them?
Again, opinion based. But yes of course, we can't question the prophets, but the rest, as described above, if one feels a higher authority could do humanly error, then yes, then he would definitely ask not challenge in a polite way for the explanation for his action taken.
What about within the family? Is it wrong for a son to respectfully challenge his father even if the son is an adult man? If either of those persons tell you to do something must you do it?
As goldPsuedo has answered, parents are to honored by Muslims at any cost as you could see from here.
But if they (both) strive with you to make you join in worship with Me others that of which you have no knowledge, then obey them not, but behave with them in the world kindly, and follow the path of him who turns to Me in repentance and in obedience. Then to Me will be your return, and I shall tell you what you used to do. (Qur'an 31:15)
I hope the above verse is clear.
May the creator guide us all.