Should I challenge my professor who thinks he's always right? One of my professors has been in the IT development fields for over 40 years. He thinks he is up-to-date with all the latest research and technology. But I believe he's not.

The problem is - he hates when a student (like me) dares to point out his mistakes or flaws in reasoning. Or when a student suggests a better (modern) solution to a problem.

How to deal with such a situation - should I keep challenging him or keep quiet until the end of semester? I don't want to lose grades (he's been known to give lower grades to students who asked him too many questions he wasn't able to properly answer).
Short answer: Probably not. 

As you pointed out, you may lose out on grades by challenging this professor. A larger problem, in my opinion, is when you (the student) approach the class with an attitude of discovering the professor's many mistakes. With this attitude, you also lose out on the opportunity to learn from his expertise. While this particular professor may not be as modern as you would like, it does not mean you cannot learn from him!

Keep quiet until the end of the semester, except when you have a valid question. And don't  approach intending to prove him wrong; approach intending to find out how you can learn from what he knows.  Ask questions because you want to learn, not because you want to prove the professor wrong. If you believe you know a better solution, it might be appropriate to ask "Would this solution also work? If not, why not?" Ask, don't tell. Your professor is human too, and most of us have a hard time always responding graciously to a smarty-pants student who thinks they know more than we do!