1. You just see a list of cores on index.jsp, but there is no way to tell that there may only be one core and an alias or something similar.
2. When shutting down the CoreContainer, if you use an alias, you will see: SEVERE: Too many close [count:-1] on org.apache.solr.core.SolrCore@3e37165f. Please report this exception to email@example.com
This is because the primary core will be closed, and then the aliases as well - even though they are the same core.