What is the proper action when peers in your field have/are publishing papers with a crucial flaw? I am in an uncomfortable position. I am beginning to do research in a particular area within my field. The body of related works are mostly done by students of a single professor. And, nearly all of it makes a crucial mistake. The works are borrowing/applying concepts and techniques from other, more theoretical and mathematical fields, yet in a way that doesn't make logical sense. Specifically, they are conflating terms, utilizing them as good sounding buzzwords, and (through an incorrect interpretation) as a criterion for the design and value of their techniques.

My work heavily uses the same concepts, yet my arguments are completely contradictory to those of my peers. So I am trying to figure out the best course of action. 

I could start by submitting a paper correcting their mistakes, but it would feel a little cruel, and would likely turn my peers against me. I could publish my works, and try to point out their flaws politely, but the flaws are so prevalent that it would still likely cause a lot of discomfort to them. I could send an email to them explaining the problems with their work, but I'm not sure how that would go. It's quite a problem, because it really invalidates the reasoning and conclusions of dozens of papers and even a text book. The professor is distinguished and well known in his field. I really don't want to be the one to stir things up, but the issue must be addressed in some way or another in order for me to publish my work.
This may seem like a cliched answer, but I believe good communication would be key. First off, you need to make absolute sure about whether or not their work represents flaws (preferably with your supervisor).  The next step I believe you should take is to contact the Professor whose team you believe has made such critical mistakes.  Discuss the issue with them and get their perspective.  If, after all of these efforts, you are still absolutely sure that there is a mistake in their work, politely inform them that you disagree with their approach/methods/technique/etc. and that you will be publishing a paper representing a different point of view and approach that presents your argument on the matter.  Mind you, don't ask their permission, it's merely a courtesy so as to show that you don't mean anything personal by it.  After that, publish away.

Finally, I should mention that I feel that there isn't really any issue at all.  If someone got mad at me for publishing a paper that disagreed with their research...that's not exactly a person I would care if they were mad at me or not.  It not only seems excessively petty, but it's also the nature of scientific research.  Great ideas and solid theories get overturned and refuted on a regular basis.  If your counterpoint to their research is solid enough to be published in a good journal, then it's good enough for them to read and consider without getting unnecessarily angry.