Just had this issue, and non of the solutions worked for me.
What I ended up doing was to quit "Calender" and the "CalenderAgent" (dunno if required). Since I don't have any local calenders (using iCloud and Exchange), I trashed all the preference files (using "AppCleaner", remember not to delete the app itself!!!).
Then I restarted the Dock, and started "Calender", and the "1" new was finally removed. There was also no reason to setup the iClound/Exchange credentials etc. again as the Calender's preferences doesn't touch those bindings.