A characteristic of the modern Evangelical church is a tendency toward personality cults, to put certain leaders on a pedestal. Now these leaders may be godly people whose desire is to serve God, or shallow purveyors of flash who only desire the public eye, or something in between. I suspect there are some in each category, and while I have my opinion in certain cases, I do not want to make any kind of blanket judgment. But I do think that there are dangers of raising even good and godly people to too high a position.
It is important that everything taught must be checked by Scripture (Acts 17:11; Galatians 1:8,9; 1 Thessalonians 5:21). This is true even of good leaders, for all of us are imperfect (Philippians 3:12-16; 1 John 1:8-10; Galatians 5:17). Often it is the errors of good leaders that are the most dangerous. It was good men, wanting to prevent the spread of heresy, who held we should not question the teaching of the church, which descended from the apostles, and thus laid the foundation of the papacy. Also, if someone is uncritically following a celebrity leader, it is more likely it will be based on external appearance than on substance. Further, people will fail us (1 Corinthians 2:1-5; Psalms 118:8; 146:3). (Even if the failure is more perceived than real, this can have the same effect.) When a ministry or a person's life is built around one person, that person's failure can have major repercussions. Also, the cult of personality can result in the creation and continuance of factions (1 Corinthians 1:10-17; 3:21-24; 4:1-5). Now there will always be areas of disagreement among Christians, but these are easier to deal with when seen as issues of fact, rather than loyalty to individuals. Also, there is the danger that human beings may be given the honor that belongs only to God (1 Corinthians 10:31; Colossians 3:22-24; Isaiah 42:8).
Now we should not throw out all prominent leaders, for according to Scripture they are a gift from God (Ephesians 4:11-16; 1 Peter 4:10,11; Romans 12:3-8). (There may indeed be some individuals who should not be followed, but this must be decided on a case-by-case basis.) Also, trusting only in ourselves can be as dangerous an error as trusting wholly in another human being (Proverbs 15:22; 26:12; 1 Corinthians 3:18). What I would suggest is putting even good leaders in perspective. One thing that is helpful here is having a broad knowledge of a large number of good teachers. Also, we should have greater respect for our more ordinary local leaders, who God has put over us (Hebrews 13:17; 1 Thessalonians 5:12; 1 Timothy 5:17), the ones we know and who know us. (Though these too can be turned into a personality cult if we are not careful.) But above all, our primary loyalty must be to God and His Word, and other things must be judged by them.