@schreck The entries with the yellow triangle are warnings. Generally, those can be ignored.
Entries with an exclamation point inside a red hexagon, are actual errors and are what would trigger the notification next to the envelope icon, as you show above.
The logging level can be changed via the 'biscuit' settings as @mib2berlin has outlined.
I have previously submitted a bug report pertaining to certain errors that were displayed in that log. It is assigned to a developer and work is in-progress.