The qualification of an elder should matter to you first because, well, you believe in the perspicuity of Scripture (if you don't, this article is written particularly to those who do hold this belief, but you are welcome to listen in). If you believe the Bible means what it says and can be taken at face value, then you by default believe it means what it says about the qualifications of an elder. But, second, if you hold to the perspicuity of Scripture, you also believe in elder authority (Hebrews 13:17). If you don't believe in elder authority, then the qualifications of the one who holds the office are irrelevant. If you do believe in elder authority (and I do), the qualifications resonate in I Timothy with utmost importance for the rest of how God planned the Church to function. The Apostle Paul presents the role of elder in the Church as one of sacred importance and influence. Pastors are influential. They hold a holy (set apart) role in the Body of Christ, and therefore, the qualifications of the person holding that office matter greatly.
For those who hold to the perspicuity of Scripture and believe that Scripture is the final authority for faith and practice for believers, when we do not obey Scripture on the issue of the qualifications of a pastor/elder, we create very large stumbling blocks for those who do not hold to those foundational beliefs.
Consider these qualifications with me. I'm not going to go through all of them for the sake of time, but I'm going to explore the ones that seem less straightforward and argue that they are actually pretty clear.
[3:1] The saying is trustworthy: If anyone aspires to the office of overseer, he desires a noble task.  Therefore an overseer must be above reproach, the husband of one wife, sober-minded, self-controlled, respectable, hospitable, able to teach,  not a drunkard, not violent but gentle, not quarrelsome, not a lover of money.  He must manage his own household well, with all dignity keeping his children submissive,  for if someone does not know how to manage his own household, how will he care for God's church?  He must not be a recent convert, or he may become puffed up with conceit and fall into the condemnation of the devil.  Moreover, he must be well thought of by outsiders, so that he may not fall into disgrace, into a snare of the devil. (1 Timothy 3:1-7 ESV)The first qualification is that an elder be above reproach. The Greek word here means that he is not open to censure, which is severe disapproval often presented in writing. (Note: all definitions here are from Strongs Concordance and Google dictionary.) Above reproach doesn't mean that an elder never receives criticism. It doesn't mean that he never makes a mistake. It does mean that his sins, mistakes, and errors do not accumulate to the point of wide, severe disapproval. When formal, written, charges are brought against a man, charges by more than one witness that reflect severe disapproval, this man is no longer fit to be in the office of elder. If you believe in the perspicuity of Scripture.
Another qualification similar to being above reproach is that an elder must be respectable. This word is used one other time in the New Testament, oddly enough when Paul is teaching about women wearing proper or respectable clothing in I Timothy 2. The implication of this word is that the elder does or says what fits the moment. Proper clothing is the clothing that fits the situation, not drawing undo attention to itself because it is inappropriate. The same goes for an elder's words and actions. He must be someone who does not draw undo attention to himself by saying/doing improper or inappropriate things that do not fit the needs of the moment.
A pastor/elder must also be hospitable. Peter uses this same word when he tells us in I Peter 4:9 to “be hospitable to one another without complaint.” This is one who welcomes people to himself. He isn't standoffish or unavailable, and he does so without complaining of the intrusion into his family life. This is a hard value to make yourself have if you aren't naturally gifted this way. But if you believe in the perspicuity of Scripture, this should characterize your life if you are an elder. Why? Because for the office of elder to work as Scripture intends it, for a pastor to shepherd his sheep, he has to be in personal contact with them. The Spirit moved Paul to set up a value system for what God intends His pastors to be, and we are ill advised to minimize something like hospitality because our itching ears prefers someone who can attract thousands with his words.
If a preacher can attract thousands with his words but is not hospitable, there is a different role in the Church for him, evangelist. But he does not meet the qualifications of a pastor/elder. If you believe Scripture.
A pastor/elder should not be violent and quarrelsome, but gentle. This includes verbal violence as well as physical violence. Jokes about beating someone up, expressing a desire to hurt someone, and threats against someone all fall in this category. I've written a lot about that here, so I won't unpack it more in this article.
I want to end with Paul's closing warning in I Timothy 3 about who should and should not hold the office of elder.
 Moreover, he must be well thought of by outsiders, so that he may not fall into disgrace, into a snare of the devil.Here, more than any of the other qualifications, I want to call on my brothers and sisters in Christ to value this qualification as a belief in the perspicuity of Scripture demands. I note conservative evangelicals falling into a bad trap of widely labeling outside criticism of evangelical leaders as persecution. That is a dangerous view. If outside criticism of a pastor/elder is mostly persecution to be ignored, then Paul has written an irrelevant phrase here in holy Scripture. But if you hold to the view of Scripture I have, you know what I have just suggested is basically blasphemy. No, this qualification matters, and woe to us who disparage it and write off outside criticism as persecution.
If a man is not esteemed outside of his congregation at some level, outside of the Body of Christ at some level, HE SHOULD NOT HOLD THE OFFICE OF ELDER. If the other pastors in his city are rising up to cry out against him. If his local newspapers, radio stations, and television stations are interviewing multiple people outside of his church who think very poorly of him, he should be removed from the office of elder. Outside public outcry against an elder/pastor is much more likely to be God's discipline than Satanic persecution, if this passage of Scripture is to be believed.
Note that almost none of these qualifications in I Timothy 3 are about how much Scripture this elder knows and how well he can teach it. Being able to teach the Word accurately is only 1 out of 14 or 7% of the qualifications Paul gives. Do not read me saying that teaching the Word accurately doesn't matter! Instead, I contend strongly that teaching the Word accurately isn't ENOUGH for this sacred role. The ability to teach the Word clearly needs to be accompanied by the fruit of the Spirit in order for a man to qualify for this precious office of sacred influence. This is why Paul give us 13 other qualifications other than being able to teach the Word – because this role is one of enduring influence over people. This is a role that is set apart by God for the long term good of His people, for their flourishing in His image. Paul gives us these sobering qualifications twice, and if you value that precious, old doctrine of the perspicuity of Scripture, you should value all of these qualifications, and in fact insist on them, in your pastor. When a man who can teach the Word but is lacking in the other qualifications is allowed to continue in this role, it harms people. It diminishes the very Word he is teaching. Those who allow him to stay in office do the same.