How are aircraft identified as unregistered?
Aircraft don't have to be actually flying for people to notice something fishy going on. In particular, there are always people hanging about at airports keeping an eye on everything going on. Furthermore (at least in the US), aircraft registration details are a matter of public record and can be easily looked up online.
For example, here is the registration detail page for John Travolta's private Boeing 707: https://registry.faa.gov/AircraftInquiry/Search/NNumberResult?nNumberTxt=N707JT
As you can see it contains complete registration details including type, validity status, expiration dates, owner name and address, and airworthiness status.