There has never been a facility built into LO to search for cross-references. The text of the displayed error is “Error: Reference source not found”. This can only be searched for using external tools, such as an extension, or by unzipping the ODT, extracting the content.xml
file, and searching the text of the XML for the error message. For example under GNU/Linux:
$ unzip -p source.odt content.xml | xmllint --format - | grep -e "Error: Reference source not found"
This will indicate if there are any broken cross-references. There does not appear to be any related open bug report for this issue, however Apache OpenOffice issues aoo#37648 and aoo#87541 seem to be requests for such a facility.
The old Apache OpenOffice XrefManager extension may also be worth a look. EDIT: Refer answer by @taylorh140.