I have been looking but have not been able to find it. Is there a way where you can put an html file in a SharePoint 2013 site collection that everyone has access to and then just reference it from different content editor web parts in different site collections?
In the OOTB content editor web part, if you specify in content link a url to a file on another site collection then SharePoint cannot retrieve content from that file. But there are other things you can do like Iframe or creating an app part and deploying it on tenant scope and using the app part instead of Content editor webpart. But these approaches will have its own limitations and is not recommended. Best way is to put the html files in some library inside the site collection.