Notes should be visible and editable on the game detail page, not the list page
The interface for adding/editing and viewing notes should be in the game detail page, not the list page.
It makes more sense to be able to add and edit notes in the detail page, where all other edits are done.
It doesn't work well having the full text of the note displayed on the list page, as it messes up the display of the list quite badly. It should be optional to hide the notes in the list page, or alternatively the interface could display just a one line of text from the note.
As notes can be usefully quite long, the full text of the note should be visible in the game detail page where enough space can be allocated, and also where it can be read in the context of other information about the game.

Thanks for the feedback! This is definitely planned as the game details page as it stands now won't exist when I rewrite that area, it will all be much more integrated into the list editing interface. You'll still be able to get to the game details but more will be available inline without leaving the context of your lists/collections. That includes a much better better "full view".