Apart from the explicit biblical qualifications, are there other important matters to keep in mind when considering a potential elder?

A man may appear to meet the biblical qualifications yet still be an unwise selection as an elder
for a number of reasons:

1. Theological disagreements. A man may be biblically qualified yet hold different theological positions than a church’s current elders. Surely, not all theological disagreements are of equal significance. Yet those responsible for choosing new elders should be mindful of the potential for division depending on the nature of a disagreement, particularly in matters of crucial pastoral importance. A church should avoid choosing leaders who will often feel conscience bound to disagree with one another in every day ministry.
2. Philosophy of ministry disagreements. Closely related to the last point is the matter of a potential elder’s philosophy of ministry. For instance, a current set of elders might be committed to the centrality of expositional preaching as the driving force of growth in a church’s life, while a prospective elder wants to direct all the church’s resources to programs are special events. A church will avoid division by ensuring that it’s leaders share some level of philosophical agreement in matters of ministry.
3. The lack of a shepherd’s heart. On the other hand, a man may be an able teacher and agree with every jot and tittle of current elders’ theology and philosophy, yet fail to personally shepherd the flock. Such a man may appear to meet the qualifications laid out in 1 Timothy 3:1-7 and Titus 1:6-9 but he will not be cut out for the intensely personal, relational burden of shepherding God’s sheep one by one.

(Some of this material has been adapted from The Deliberate Church by Mark Dever and Paul
Alexander, pages 141-142, 146-148)