Our focus here is primarily on elders, but I would like to briefly mention the subject of deacons. I believe there is much confusion on this subject, and I would like to suggest a few things that could be helpful. First of all, the term "deacon" is not a translated word. The Greek word is "diakonos," and in the passage in I Timothy, the translators chose not to translate the word but rather leave it up to the reader to apply it properly. The word "deacon" basically means "servant," or one who executes the commands of another. It is often translated as "minister" or "servant." Obviously, that is quite a broad term, so further clarification is required for us to know what kind of service or ministry is intended.
The first passage most go to is found in Acts 6, where seven men "full of the Holy Spirit" were chosen to address the problem being faced by the early church, of certain widows being overlooked in the distribution of food. Although the word "deacon" is not found in most translations, the word is there in the original. However, it is not just used to apply to the seven men who "served tables," but also to the apostles.
There are slight differences in the root word, but notice how the word "deacon" is used. "Then the twelve summoned the multitude of the disciples and said, 'It is not desirable that we should leave the word of God and serve [deacon] tables. Therefore, brethren, seek out from among you seven men of good reputation, full of the Holy Spirit and wisdom, whom we may appoint over this business; but we will give ourselves continually to prayer and to the ministry [deacon] of the word'" (Acts 6:2-4). In other words, there was a "serving" of tables and also a "serving" of the word of God by the apostles. Thus Stephen could be called a deacon because he was serving in the matter of food for widows, and Peter could be called a deacon because he was serving or ministering the word of God.
If we go back to the passage in I Timothy then, we have qualifications for deacons, who are "servants" or "ministers." For several reasons, I believe that the primary application of the qualifications in this passage is for ministers of the word of God. One indication is I Timothy 3:9 which says that deacons must hold the "mystery of the faith with a pure conscience." I would say that is a reference to those who minister the word of God. This would include prophets, teachers, and evangelists. An elder is not necessarily one of those, so I believe Paul is giving us similar qualifications for those men (deacons), after listing the qualifications of elders.
Another reason I believe this passage applies primarily to ministers of the word of God is that they occupy a very prominent place, and thus a clear testimony is very important. They lead the church publicly by proclaiming the word of God. A man who does that without a good testimony brings great reproach on the testimony of God. His ministry cannot be effective. Not only will it not be effective; it will have a deadening affect on the assembly because people may listen politely while inwardly not receiving it, and likely become hardened to the word.
In general, I think we can say that anybody who "serves" in any capacity should be qualified for the service they render. However there may be some areas of service that a member is qualified to function in without meeting the full qualifications of a minister of the word. For example, a brother may be very faithful in financial areas and be helpful in attending to some needs of the gathering. Yet he may be divorced and unable to change that condition. Based on scripture, this would disqualify him from serving as a minister of the word, but not for serving in the area of finance. That is just one example, but I think there could be many others of a similar nature.
The main point I wanted to bring out is that we may have men with a gift of teaching or other public ministry, but that does not necessarily mean they will function as an elder. They may function as a deacon (minister), and if they do, they should "be tested and then let them serve." They also may be recognized by the church and set apart to fulfill their calling or ministry in the church. While some may not have this understanding of deacons, I offer this for us to consider before the Lord.