I have a friend with a small business with a website. He asked me if he should make a put a section on his landing page under the fold that with his most recent review (or something along those lines). Specifically, he wants to know if that's the most efficient use of his time. Is there a list or such of things google values compared to each other, so that these kinds of answers could be easily answered?
Based on my own experience, I see no reason why changing part of the page periodically would have any benefit to rankings. There are other, much more important factors in how/why/where a site ranks.
Certainly, it's good to have new content added to the site regularly. But just shifting around one portion of one page doesn't present any real benefit IMO.
Some of my best ranking pages historically virtually never change.