When viewing an inactive object (as an administrator), the object looks no different from an active object when Solr is having problems. You see the object as normal, and in the metadata display area you get the error:
"Document not present in Solr while generating the metadata display for [PID]. Try reloading the page, or contact an administrator if this issue persists."
Because Solr problems are not uncommon, there should be a quick way to differentiate inactive objects from regular objects experiencing indexing problems.
Proposing a Drupal message at the top of the page when viewing any inactive object, saying something to the effect of, "This object is inactive and is not currently indexed by Solr."