Currently, the two most important dashboard widgets, "system status" and "last n issues", can be filtered by trigger severity, but the setting affects both/all widgets.
It would be very useful to see all severities in the the system status matrix, while hiding unimportant events from the last n issues list.
I'm intentionally calling the widget "last n issues", see
ZBXNEXT-1029. Also related, ZBXNEXT-2819 could be addressed at the same time: Filtering away "all-green" hostgroups from the system status matrix could/should be configurable from the widget's popup menu.