When I’m trying to log in with a wrong password, I get the following error:

Error in JQuery.ajax when submitting a form: SyntaxError: Unexpected token <

This happens only when I’m filling in a wrong password. When the right password is entered, I get logged in.
How can I solve this?

Please do the following:

open functions.php in the Avada theme folder.
Search for this line: add_action( 'init', 'avada_load_login_redirect_support' ); and comment it like this:
// add_action( 'init', 'avada_load_login_redirect_support' );

Then it should work.

The problem was that Avada placed an redirect when a login fails, and return an HTML page. the Ajax Request expects an JSON response but gets an HTML and tries to parse it. And then gives the error.