The word ἀνεπίληπτος is particularly relevant because it functions as a header for the rest of the list of characteristics. The most common translations for this word are above reproach (NIV, ESV, NASB, CSB) or blameless (KJV, NKJV). So what does this word mean? Does it mean that an overseer can never sin in any of these categories? This might seem to be implied by transitions such as “without fault” (GNT).
This word is only used three times in the New Testament, and the Greek word is not used at all in the Greek translation of the Old Testament. In fact, all three uses of this word in the New Testament occur in 1 Timothy. In 1 Timothy 5:7, Paul used this word in the context of commands for Christians in caring for widows. Paul claimed that Christian children and grandchildren were to the the first to care for widows in their own families (5:4). So “true widows” in Paul’s eyes were not just those who did not have husbands, but true widows were those who had no family to care for them at all (5:5). So the widows who fell under the direct care of the church were those who had no family to take care of them.
1 Timothy 5:7-8 contains a contrast that helps us understand what ἀνεπίληπτος means in that context. First, Paul said that Timothy was to command these things so that they might be ἀνεπίληπτος. These commands are commands for Timothy to give to the church, so that the church might be above reproach in how she treats widows in her midst. In 5:8, Paul shifts the focus to those who profess to be Christians but who do not provide for their own families. Paul says such people have denied the faith and are worse than unbelievers. So in this context, the ἀνεπίληπτος or above reproach of 1 Timothy 5:7 means that Timothy was to teach the church the proper way to care for widows in their midst so that the charge of denying the faith and being worse than unbelievers could not rightly be leveled against them.
Paul’s final use of this word occurs in 1 Timothy 6:14. Paul charged Timothy to “keep the commandment, unstained and above reproach until the appearing of our Lord Jesus Christ.” This concluding charge to Timothy was a call for Timothy’s life to demonstrate the kind of character that flows from those who trust in God. Certainly Paul was not demanding sinless perfection, but he was charging Timothy to live in such a way that there was no stain on his character, no charges that could be brought against him that would disqualify him from the ministry to which he had been called.
In sum, ἀνεπίληπτος in 1 Timothy 3:2 serves to set all of the following characteristics in their context. Paul is not demanding sinless perfection from church leaders, but he is saying that church leaders should live in such a way that they cannot rightly be charged of violating any of these characteristics. To use but one example, the overseer might get in a quarrel, but he must not be someone who is quarrelsome or known for quarreling. He will not be perfect, but his general pattern of living must be sufficient to serve as a model for the rest of the church.