dpkg -l | grep -v "^ii"
This shows all packages that are installed but in a "weird" (not 'ii') state. That's exactly what the Icinga check runs as well, so to get that back to OK you want to make sure all packages are in "ii" state.
What the other states mean exactly you can see at the very top of the output. One letter is the desired state and the other the current state.
Desired=Unknown/Install/Remove/Purge/Hold | Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend |/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
Either remove broken packages (apt-get remove --purge <package>" or fix half installed packages (apt install <package>) or try to remove and reinstall it.
If it happens on a lot of servers at once or unsure open a ticket.