With regards to authority does the Five Fold Gifts have more authority than those who operate in another gift? When someone in leadership is wrong can a layman point out their error or is that specifically done by someone else in leadership?
I'm answering your second question "Can the Five-fold ministry be corrected by someone who is not that?" because I think that is the main thing you are asking rather than what you have worded in the title and opening line. In doing so, I note that the The wording of your question presumes a contemporary Charismatic Protestant point of view, so I'm going to frame my answer according to that. (But I'm going to take my time during the next few days).
Yes! If you follow that theology, then the Bible should be your chief authority (You believe in Revelation and other things like experience but that is submitted to scripture). There are some points of consideration. The main one is this someone who keeps watch over your soul (Hebrews 13:17), such as a pastor, bishop etc.? If yes, then it would probably better for someone else to that. IF you are a person who has only been a Christian for a few years this is especially true (1 Timothy 3:5-6). Saint Paul uses the language of fatherhood describe this sort of relationship (insert scriptures). So if you do so to someone like that it is best to do much like you would a close relative (Father, favorite uncle etc.).
(I'm assuming you are talking about something more than just pointing out that minister misquoted a Bible verse. If it is just that making a basic factual mistake then there should be no problem correcting the person than any other person). Saint Paul uses the language of fatherhood describe pastor
1) To start with the word for Truth in the New Testament is Alethia. The Lexical meaning of that Greek word refers to objective truth, "Truth in reality". So if you believe that you have some sort of objective evidence against something this defintion should encourage you to present it. I will also point out that this truth also fits certain laws of both logic and secular epistemology too.
2) You should based on the consideration of the many verses relating to false ministers. (And note that the various passages in the Bible that speak of anti-Christs can also mean false "Anointed ones, which can be seen as prediction not just of thee anti-Christ but false ministers who claim authority via "an anointing"). Here are just a few examples, but many more exist in the New and Old Testament.
Matthew 24:24 ESV
For false christs and false prophets will arise and perform great signs and wonders, so as to lead astray, if possible, even the elect.
1 John 4:1
Beloved, do not believe every spirit, but test the spirits to see whether they are from God, for many false prophets have gone out into the world.
2 Timothy 4:3
For the time is coming when people will not endure sound teaching, but having itching ears they will accumulate for themselves teachers to suit their own passions
For such persons do not serve our Lord Christ, but their own appetites, and by smooth talk and flattery they deceive the hearts of the naive.
3) In the Bible there exists some basic common sense, rules of thumb ("Economies" in theology) for correction. Things done in public are handled in public, while things done in private are handled in private (at least initially).
There also exists a similar common sense when it comes to giving and taking correction. People acquire authority by being under authority. People can also expect to receive back the same kind of rebukes and other correction that they dish out (Matthew 7:12 and Jesus interactions with the Judgmental Pharisees are the best example of this truth). So in everything, do to others what you would have them do to you, for this sums up the Law and the Prophets.
4) We are called to look out for the public good. To be our brother's keeper and watchers on the Wall (Ezekiel 33:1-6)