But I'd start with laying out concrete things, rather than "embarrassed and ashamed".
If you make this sort of contact, though, I'd recommend against saying anything like "[you] should be embarrassed and ashamed to have such a professor." Stick to facts.
Also, note that even very accomplished and intelligent people can make mistakes when they speak. I don't know what "obviously incorrect" facts you professor is stating, but I've had good professors bumble words and even ideas. And I know (as a former student) that students love discovering and pointing out those errors. Even if they have no real bearing on the quality of education being delivered.
I had a Calculus prof who was worthless. She would literally read from the book and copy it verbatim on the blackboard. No questions. If you had a question you had to write it down on a piece of paper and leave it on her desk. If she could get around to it the question might be answered in a day or two. Students had no way to fire this prof or get her reviewed and replaced. We had to endure the torture and learn on our on.