I am having a very similar issue, so I hope one of the more knowledgeable users is able to provide some guidance.
I have created a series of address locators, based on TIGER, for several counties in Minnesota. After sorting through the unmatched records, I was able to identify a general pattern �?? namely �??incorrect�?� zip codes. (I say �??incorrect�?� because many of these addresses/intersections have been confirmed through MapQuest/Google Maps/USPS, but the TIGER data is showing a different ZIP.) I would like to run the address locators *without* ZIP info on our second go around, to pick up these remaining addresses/intersections. However, as apj283 mentioned, any time I try to leave out the ZIP field, no records will match.
I feel as if I�??m missing something very obvious? Admittedly, all I know about geocoding (and ArcGIS, for that matter) is what I�??ve managed to teach myself, but I feel like there�??s probably a simple resolution just staring me in the face.