The professor for one of my classes has no direction
Yes, you should raise this with the department, either with the Undergraduate Director or the Chair. The problem is not Prof. Johnson's unfamiliarity with the LMS--as a new faculty member, that is understandable. But you should restate what you said here about not teaching the assigned material. 

You mention online quizzes that were given to him. Are they being offered and graded? If so, is the grading fair? If not, what assignments will your course grade be based on? 

If the lessons are not being taught, students cannot complete the assignments successfully. That is the kind of issue the department's administrator will be concerned about, because they do want you to get a serious education in every class. And they know that the grading scheme in the syllabus, as well as the learning objectives, are contractual issues that have to be fulfilled. 

In talking to the administrator, stay focused on teaching performance issues only and avoid anything personal. You are supposed to be learning something critical about the history and practice of public speaking, and you should have an opportunity to demonstrate that learning fairly, through tests or papers. If that is not happening, the department's administrators need to know. The sooner the better.