Where would information for this error be stored at?

This looks like a re-occuring issue that many people are experiencing at the moment, firstly if you click on the toggle button on the left of the event you will be able to see the error.

You will also be able to see the error in Settings → System Info → Log.

This post probably covers your issues: mautic.ERROR: [MAIL ERROR] Expected response code 250 but got an empty response - #7 by mikew

@rcheesley I have now seen three posts today on the same/similar issue, maybe it is worth merging them all ?