One oddity not mentioned here that I came across recently, (which probably would go into one of those "things programmers don't know about postcodes" blog posts).

A system that used Postcodes for geocoding (not a great idea) was choking on PO Box codes that belong to districts (such as W1A in the London W district), but don't really correspond to actual street addresses.

This also catches some people out who will unintentionally use the PO Box postcode alongside the full street address of a business for example.

I've also worked on the TV Licensing systems (yes, the one that sends you scary letters every year). That has its own database of postcodes and addresses and I got to spend lots of time on the funny rules there.