How to automatically add custom classes to headings in content area

Yes, there are a couple of ways you can do this. One is by creating a filter in the functions.php file, like what is done here: https://stackoverflow.com/questions/10468697/how-to-add-a-class-to-a-html-element-using-filters-in-wordpress

The other would be to use Javascript/jQuery to add classes to all the headers post load. Using the php variant would be more elegant, though.