The two words "point out" and "mention" are so close that I can call them synonymous words; but I see some slight nuances when it comes to use each one. I have read so many examples and dictionaries and found out that you 'point something out' if you think it is important that the other person should know this. For example, if you see a mistake in a report, you should point this out to someone. This means that you draw someone's attention to it. It's like pointing your finger at something to draw attention to it. However, I wonder which examples below (made up or taken from OEDs,) which are all correct with "mention", can work with "point out" either or they would sound unnatural to you?
- He mentioned that he was having problems, but he did't explain.
- He casually mentioned that he was quitting his job.
- That's her right to know about the company's decision. She myst make a decision about her future soon as possible. Although, it's hard to tell her, but I'll mention it to her when I see her tomorrow.
- My wife mentioned seeing you the other day on the street.
As you see, in all cases above, someone is trying to inform something apparently important to someone else. So, this is logical that "point out" should work here without any change in meaning. I would really appreciate it if you help me find out about these cases and the nuance between these two.