Please understand that I was not there, so I can't comment on whether the elder did right or wrong in asking another man to speak that day. I definitely can't comment on the elder's qualifications. But what I can address is the issue of how to handle false teaching in a service.
"Let two or three prophets speak, and let the others judge. But if anything is revealed to another who sits by, let the first keep silent. For you can all prophesy one by one, that all may learn and all may be encouraged. And the spirits of the prophets are subject to the prophets" (I Corinthians 14:29-32).
Though Paul was addressing prophets speaking during an assembly, I believe the principles are basically the same whenever someone addresses a congregation with teaching.
The first thing to remember is to be polite. Depending on the circumstances you can either indicate that you would like to address the congregation next, or you might stand and wait to be acknowledged. Then ask if you might ask a question or two to clarify what is being said, or ask if you might point out some scriptures on the topic at hand. What you don't want to do is talk over the false teacher. That gives the impression that you have lost control. Now, he might interrupt you and when he does, be quiet, wait for him to finish, then ask politely if you might continue your point. "For God is not the author of confusion but of peace, as in all the churches of the saints" (I Corinthians 14:33).
Handling who speaks next in this manner gives a greater chance for polite discourse as opposed to a shouting match. And if you can keep your cool while the other loses his, you might have a better chance of persuading others of the truth.
If other men in the audience also wish to have a say, then allow each to speak one after the other. As a preacher, you have the responsibility to see that truth is taught. "Speak these things, exhort, and rebuke with all authority. Let no one despise you" (Titus 2:15). This is also responsibility of the elders. "Holding fast the faithful word as he has been taught, that he may be able, by sound doctrine, both to exhort and convict those who contradict" (Titus 1:9).
Just because something is said from the pulpit, it does not follow that it cannot be questioned. Notice that the prophets were to judge what was being said. Why? "Because many false prophets have gone out into the world" (I John 4:1). The prophets served as checks regarding the truth of what someone claimed was from the Lord. This also helps clarify Paul's next statements: "Let your women keep silent in the churches, for they are not permitted to speak; but they are to be submissive, as the law also says. And if they want to learn something, let them ask their own husbands at home; for it is shameful for women to speak in church" (I Corinthians 14:34-35). Women are not allowed publicly question what is taught during a service. However, consider the implications. Men may question so long as it is done in a decent and orderly fashion. We've lost that insight over the years.
In regards to the elder who invited this man to speak, what needs to be determined is whether he knew this man was going to speak falsely on a subject in advance. He might have had no idea that someone he heard was a faithful preacher actually held to false doctrine. So to accuse the man of making a mockery of the church is making assumptions that I don't think you can firmly prove. "Do not receive an accusation against an elder except from two or three witnesses" (I Timothy 5:19).
As a preacher, I've never considered myself in control of the pulpit. I appreciate it when others in the congregation wish to bring lessons. And if someone is visiting whom I know as a faithful preacher and I know it in advance, I will usually ask him if he would like to speak. I end up doing the asking because we don't have elders at La Vista at the moment. You might look at it as a break from preaching, but I see it as an opportunity to hear someone else's views. Plus, I must remain on duty because if something is taught incorrectly, I have a duty to straighten it out.