How large may included parts from other people's work be in an academic paper? Of course, it is absolutely important to quote all thoughts that did not originate from the author. This makes one think that it would be OK to include works of others when referencing them correctly.

For example, consider that one had that really great list of problems that also apply to your own paper. Is it legal and/or legitimate to write about that list, include the key points in your work and reference the original author?

I am facing that situation where I want to include some key aspects but quoting all of them and describing them individually feels like copying too much, even though I explicitly state that the aspects originate from another paper with referencing to it.
You can include any material that is published as long as you appropriately cite the material (source). If you think any phrasing made by the author(s) is key, then you can do it as a quote where the text is reproduced in verbatim. If you do not use quotes you need to rephrase the text in your own words since it would otherwise be considered as a form of plagiarism. So, just be careful with referencing and quotes if necessary. It is better to have cited one time too many than the opposite.