I would consider creating a new popup page that lists all of the objects that are missing a piece of data. This also allows you to expand a bit more by adding extra details about each object i.e. what exactly is missing, show a specific error against an object, and maybe have a button that takes you to another page where the user can fill in the blanks.
Since you can’t pass a list of objects to a page, you can achieve this by creating a dummy entity to be passed to a page, and associate objects with it which need to be shown on the page. Once the page opens, you can have a data/template grid/list view showing associated objects there.
You can also put everything in ‘Show Message’ action as you’ve mentioned but this way you lose the ability of adding extra bits to make the user experience better.