The meaning of "note" as a verb

Solution 1:

If you look it up in Merriam-Webster, it is clearly explained that "note" as a verb could have the following 4 basic meanings: 1. notice 2. record in writing 3. mention 4. show

So, it is the context that tells us which of the meanings it bears.

You may want to check out this link for details: https://www.merriam-webster.com/dictionary/note

Solution 2:

1 and 2 above both refer to a more detailed observation; either it stood out to the observer (2), or the audience should take care to make it stand out to them (1). The subject helps disambiguate the meaning here, because it identifies who acted or to whom the action happened.

Solution 3:

The professor noted in class that their valid ranges of usage were complementary.

Most people who read this would assume that the professor was mentioning it or pointing it out for their students. If the professor noticed it for the first time in class, i.e. had a sudden epiphany about it, it would probably be phrased with a different verb, e.g.:

The professor realized in class that their valid ranges of usage were complementary.