How to change the order (priority) of registered filters (or actions) (e.g. for the_content)?

If you know the existing callback and priority you can just remove the filters and then add again at a different priority:

remove_filter( 'the_content', 'convert_smilies', 20 );
add_filter( 'the_content', 'convert_smilies', 30 );

remove_filter( 'the_content', 'capital_P_dangit', 11 );
add_filter( 'the_content', 'capital_P_dangit', 20 );

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