What is the duty of a Christian if he/she hears a false teaching from another local church? We were invited to attend another local church and found the message we heard from the pastor to be false teaching (i.e. that we are Hebrew not Gentiles, asking the audience who wants to be filled with the Holy Spirit like the pastor was in control of it, etc.)
According to the Bible, all believers have a responsibility to avoid false teachers and false teaching, while pastors and teachers have an additional responsibility to point out false teaching to the brethren:
1Tim. 4:6 In pointing out these things to the brethren, you will be a good servant of Christ Jesus, constantly nourished on the words of the faith and of the sound doctrine which you have been following.
2Tim. 2:14 Remind them of these things, and solemnly charge them in the presence of God not to wrangle about words, which is useless and leads to the ruin of the hearers.
2Tim. 3:1 But realize this, that in the last days difficult times will come.
2Tim. 3:2 For men will be lovers of self, lovers of money, boastful, arrogant, revilers, disobedient to parents, ungrateful, unholy,
2Tim. 3:3 unloving, irreconcilable, malicious gossips, without self-control, brutal, haters of good,
2Tim. 3:4 treacherous, reckless, conceited, lovers of pleasure rather than lovers of God,
2Tim. 3:5 holding to a form of godliness, although they have denied its power; Avoid such men as these.
Titus 3:8 This is a trustworthy statement; and concerning these things I want you to speak confidently, so that those who have believed God will be careful to engage in good deeds. These things are good and profitable for men.
Titus 3:9 But avoid foolish controversies and genealogies and strife and disputes about the Law, for they are unprofitable and worthless.
Titus 3:10 Reject a factious man after a first and second warning,
Titus 3:11 knowing that such a man is perverted and is sinning, being self-condemned.
The repeating counsel of Scripture is to avoid the false teachers, pointing out their errors to others, and seek for better things.
However, there is no requirement to personally challenge or correct a false teacher, nor are we charged with seeking to remove such men from leadership positions or persuade others to do so. Though it may be appropriate to raise concerns through some formal process, the general biblical requirement is simply to flee the false teaching while pointing it out to others. Share your concerns with your friends, but do so in love.