It seems to me that we are always looking for faults and weaknesses in others... are we just covering up inferior feelings within ourselves?
By and large, everything we condemn in others is just a way of hiding a similar character within ourselves.
I know that when I look at people, I end up judging them on superficial things. I also know that this hurts my relationships as well as myself. I want to stop. How do I turn this judgmental nature off whenever I see something in someone that doesn't meet my approval?
The idea is not to try to turn off this nature, but to come awake to the actual experience of yourself that you have in these moments. Resisting thought does nothing. Learning to "taste" what judgmental thoughts bring to your inner table will teach you to leave the establishment called yourself.
It seems that all I am seeing of late are the negative things in people and how much suffering this causes. I am not very comfortable with this development in myself, as I usually like to stress the positive. Will I get past this stage, or do I just have the wrong point of view?
One of the wonders of true spiritual work is in our awakening to the actual nature of the people around us. Don't avoid this development, or think that something has gone wrong within you for all the wrongness you now see around you. Gradually, as you become more inwardly sensitive to the manifestations of people -- and realize that you recognize what you do about them because of what you can see in yourself as being true -- then real compassion is born. This same higher inner awareness grants you patience and new forms of consideration, because now you realize just how much pain everyone is really in. Keep going.
The more I think I know about true spirituality, the more I become easily aggravated by the seemingly false or inconsistent behavior of others. I can sense that part of my anger is seeing the inconsistency and false behavior in myself. What is the right way for me to handle these moments?
Stay with yourself. Don't put yourself into what you observe. It doesn't matter what anyone anywhere is doing or saying relative to your potential for inner development. The expression "The buck stops here" is valuable as long as we understand it to mean that these recurring blasts of unconscious energy we experience in moments such as these are to remain conscious within ourselves. We must not attribute their cause to someone or anything else outside of us. When we work with this truth and its instruction, then we begin to die to the blame-casting nature.