It seems that you can only search for a name or a company name in iOS's Contacts app. You can't search for an address, a zip, a note or any text outside of those fields. The same holds true for searching in iOS/Spotlight.

Besides the third party app for finding contacts via phone numbers mentioned before on this site, is there any way to search for an address, a city, a zip code, or a note in the Contacts list in iOS?

This seems like a glaring oversight by Apple engineers. Is there a reason for this?