You can use the search builder to search any fields that are empty or null:
civicrm/contact/search/builder?reset=1 (should be in your Search menu item)
We also use a report for tracking a very similar thing. We use the Contact Report (Summary) Template (it might say Constituent instead of Contact)
As long as you've built the field to be searchable, it will be included in your report (this is a check box at the bottom of the field)
You can then select the fields your interested in seeing and filter the report to show those where the field "Expiry Date" = This Month
We trigger this report to be emailed on the first of the month so you can immediately see who requires renewing.
As you're using a relative date, it will always be current for the month you're in.
You can also build a smart group this way, and always have a current list of those who will expire this month which you can use in searches / mailings as you need.
Hope that helps.