How do you respond to criticism?
It depends on how serious the criticism is, whether the person is serious, and whether they are competent and respectable.
If I hear that a person I respect or a person who is careful and thoughtful is criticizing me, then I want to look at it and ask if they see something that makes my view unbiblical. If so, I don't want to stay there. I hope, with regard to serious criticism from people who are responsible readers of the Bible, that I would listen and grow.
There is a lot of criticism that doesn't seem to demand that kind of careful attention though, because the person is just missing my message. They are saying things that I've thought about a hundred times and worked through over and over; therefore, I don't think their criticisms are right, and I don't lose a lot of sleep over it.
And I've never had anyone criticize me who was in the position of mounting some huge crusade to try and kick me out of my church. I've never had that kind of existential crisis where the opposition against me feels like it is going to have repercussions anywhere significantly. So I don't lose any sleep over it, by and large.
If you believe that someone else is teaching something wrong, what is a proper way to respond to perceived mistakes?
A lot of that has to do with the relational dynamics. If they are in my church, then it is my pastoral duty to pursue them, talk to them, confront them, and exhort them. That is what a shepherd is for. It might lead to some kind of discipline if it is serious enough and they are unrepentant, but in that context it is generally a personal pursuit.
As the concentric circles move out relationally then I should deal with a person more or less directly or indirectly. If someone has published something on the web or in a book, then they are fair game to be spoken about publically. But if there is a relationship there, then I think that following through on that level is really valuable.