Is it generally worth the time and effort to challenge incorrect exam test items?
Though the fact that I, a student, was the only person who realized the mistake and sought to have it fixed reflects very poorly on the quality of the institution. 


Yes, it does.  


  I believe the material should be correct so that future students do not suffer the same frustration nor are taught improper concepts. 


Of course it should.  But ultimately, the correctness of the course material is the responsibility of the instructor, not your responsibility.  


  I have had to fight tooth and nail to correct some of the material.


That strikes me as quixotic.

It's certainly reasonable, and helpful to future students, to report errors that you find in the course material.  The instructor should then either fix it, or discuss with you why the course material is actually correct.

But if the instructor does not seem interested in doing so, then it's probably a waste of your time to "fight tooth and nail".  Unfortunately, crappy courses and instructors exist, and it's not your job to fix them all.  Simply quit giving them your money and attention: look elsewhere for better courses.  If you like, leave negative reviews.  Future students would be helped by having the errors fixed, but if the courses are as poorly managed as you describe, they would be even better off not taking them at all.