This usually happens for MySQL-based tables with server-side processing turned on.

Please check if you have a complicated query with JOINs, calculated columns (e.g. ” SELECT mycolumn*2 AS mycolumn2″), or some custom column aliases (e.g. “SELECT mycolumn AS ‘some/weird/name’). If this is the case, please either create a MySQL view (in PHPMyAdmin or similar MySQL DB manager) and build a wpDataTable based on this view.

This can be achieved with adding database name in front of a table name in MySql query.
For example:
SELECT * FROM database_name1.table1_name tb1 INNER JOIN database_name2.table2_name tb2 ON tb1.field_name=tb2.field_name

Just please make sure that MySql user that your site is connecting with has the right privileges for every database in MySql query.

If you are using separate MySql connection option to connect to mysql database, you can test if connection can actually be established with “Test MySQL settings” button.
If connection can’t be established, first please make sure that all entered values needed for connection are correct.
Also make sure that MySql server is allowing remote connections and that MySql user that you are trying to connect with is allowed to connect from your sites host(IP address).