Runtime administration: Alfresco enterprise allows to perform certain actions on Alfresco subsystems without restarting the server. This allows you to be very fast during debugging/developing and also making changes in production environment. Also you can access the JMX interface that supports JMX Remoting.
There is no consistency check or update, until you restart the server (during the startup you have to validate/check/rebuild your indexes). There is an option in alfresco.global.properties (or the original repository.properties config file) for that. If you have some inconsistencies in the Alfresco Community index, you're gonna have a bad time xD.
Alfresco Enterprise has specific license for clustering your architecture, the Community edition doesn't support those systems. Replicate and cluster Alfresco is one of the main improvements in performance/scalability/availability you could achieve.
The storage policies allow you to use Content Store selectors in Alfresco Enterprise. You can manage a primary and a secondary file store, and map/connect these stores in your architecture. The Community Edition allows you only to use one content store at a time.
These include everything inside Alfresco (Spring Framework, Apache-Lucene/Solr, Tomcat, and so on), because with the Enterprise license you have also the full support with everything inside the Alfresco package. The difference is that the Community is based on daily builds, supported by community, and therefor not guaranteed. The Enterprise support helps you resolve many problems that you might encounter during developing and in production environment, not only Alfresco related, but also on some configurations on supported platforms (Windows/Linux), your web application servers, and so on.