How should I address a professor's inconsistencies? "How do I address the following incidents before the end of semester, without alienating the professor whose good graces I rely on to pass his class?"

I have a professor who is quite friendly, and obviously more knowledgeable on the topic he is teaching than I am. However, he consistently makes major errors, and is very inconsistent with his statements, assignments and testing. I have been tracking these inconsistencies, as they make it very difficult to keep up with the class. Copied and pasted from my notes:




  A list of Professor X’s major inconsistencies in Math 555, Complex
  Variables
  
  As a fellow student in my class commented, Dr. X's inconsistencies are
  “astounding”. So, I decided to keep track of them.
  
  Incident 1 
  Professor X, in two class periods, could not prove the
  sufficient conditions for differentiability (i.e. converse of
  Cauchy-Riemann). he made errors so numerous while presenting the proof
  that he never finished it, and told us to just look at it in the book
  and practice it at home.
  
  Then, when asked about the proof in the book, he said that the proof
  was incorrect, but did not provide any suitable
  explanation on how the students might approach doing it correctly. 
  
  So, he could not do the proof himself, could not explain why the one
  in the book was wrong, and yet he required us to complete the proof
  for homework…
  
  Incident 2
  Midterm #2 was held on a Monday. The Friday before the
  test, he explicitly told the entire class to bring a handwritten sheet
  listing all of the algebraic properties of the Logarithm and
  Exponential functions of complex numbers. Further, on Friday before
  the test, he told us that the test would cover all of chapter 2 and
  through section 31 of Chapter 3.
  
  When the class arrived to the test on Monday, we were all surprised to
  see written on the test, “Turn in homework for sections 34-36”. These
  sections covered trigonometric identities and hyperbolic functions of
  complex numbers not log(z) or exp(z). 
  
  Instead of admitting his mistake, he gave zero credit for the
  properties we turned in. Further he said that we should have proved
  them, when he only asked us to list them.
  
  He then proceeded to tell us that if we wanted to get credit back, we
  could prove them and turn them in again. I explicitly asked in front
  of the entire class “Do you want us to prove the properties of Log and
  Exponential functions, or do you want us to do Sections 34-36, as was
  written on the test, or both?” He responded that he wanted the proofs
  of the Logarithm and Exponential function identities. So that’s what I
  did. 
  
  When turning them in, he did not accept them, because he wanted the
  trigonometric identities instead. So, after wasting hours of my time,
  again, I find myself in the library doing work that he did not assign
  instead of moving forward to reinforce topics that we are now
  covering.
  
  Incident 3 
  When reviewing test problem 3 (determine the derivative of Log(z)) he told us 
  that we should have used the polar
  form of the derivative: f ‘ (z) = exp(itheta)(u_r + iv_r) that we
  derived in problem 1. 
  
  The problem is, he didn’t ask us to derive that formula in problem 1.
  When I pointed this out, he looked at me like I was crazy. So I went
  to his office hours and very politely showed him the test and asked
  “When did we derive the polar form of the derivative in problem 1”. So
  he proceeded to do problem 1, and sure enough the polar form did not
  come from it. It took the answer to problem 1, plus an extra page and
  a half of derivations to arrive at the required formula to solve
  problem 3.


So, I want to address this because it is driving me crazy, but I am unfortunately a fairly poor student when it comes to test taking (high levels of anxiety). I rely on the fact that my professors like me and see how hard I work in my classes, to get the extra few sympathy points that often are the difference between passing and failing.
This is an uncommon situation. It happens that a professor has a blackout in front of class or screws a proof - but this sounds much worse.

It is hard to tell from the distance, but to me it seems like the professor is having serious problems (maybe health issues, personal issues, ...) distracting him.

I would suggest talking to another trusted faculty member (if you don't know whom to adress: There are usually dedicated ombudspersons at every department / university) and tell them your observations.