An usability upgrade would be to allow port ranges, for example I wanted to try 0-1023.
Google for "scan ports" and you'll discover plenty of people offering this service already.
http://www.sans.org/security-resources/idfaq/port_scanning_l...
Knock on someone's door? Once is fine, more than about 20 times [in a day] is likely to be seen as a nuisance. You'd have some sort of exclusion order long before you get to 2^16 times.