When you share a Google Doc, there's an option to give everyone in your domain permission to view and edit the document. As far as I can tell, there isn't an equivalent option for Google Calendar. There's an option to "Share this calendar with everyone in the organization," but all the options are read-only, there's no option to allow others in the organization to add or edit events. Am I missing something? Is this something the domain administrator can enable?
You can use Google Groups to solve your problem. Have the Super Administrator create a group containing all users in your Google Apps account, then add this group's email address to the calendar with the "Make Changes to Events" permission level.
One complication is that giving a group permission to a calendar doesn't add that calendar to the user's calendar ACL - in other words, they will not see it show up in their calendar list after you give the group permission. Your Super Admin can use the powerful Google Apps Manager tool to add this calendar to the calendar list of all users using the below syntax (source), replacing
<calendar email> with the actual email of your calendar:
gam user all users update calendar <calendar email> selected true
Also, as you noticed, there isn't currently a Super Admin setting to allow all organization users to modify a calendar - only to change the visibility: