I am having the same problem.
Brand new iPhone 4S. Never had an iPhone before.
There is no PLUS sign. The top has 'All Calendars' - and that's it. In the system settings there is no option for Default Calendar.
I neither have nor want iCloud.
Wondering if it's defective and I should return to the AT&T store and get another one.
Any assistance would be appreciated.
Just spoke with a Senior Tech at Apple Support who solved the problem, for me at least, and it involved disabling Calendar under my Gmail account.
Settings -> Mail, Contact, Calendars -> Accounts.
One of my accounts is Gmail.
Gmail -> Mail, Calendars, Notes. Mine were all turned 'ON'
Turn OFF Calendars.
Go back to Home->Calendar-> and the Plus + sign is there and editing is fine!!!!!