Showing a JDialog whenever there is an exception
At first I had two different methods for each one but now I combined
  them into one.  


I would have made 3 methods instead of one.  

public static void showError(String errorMessage) {
    showError(errorMessage, "Error!");
}




public static void showError(Exception exceptionError) {
    String errorMessage = "Message: " + exceptionError.getMessage()
                + "\nStackTrace: " + Arrays.toString(exceptionError.getStackTrace());
    String title = exceptionError.getClass().getName();
    showError(errorMessage, title);
}




public static void showError(String errorMessage, String title) {
    JOptionPane.showMessageDialog(null, errorMessage, title, JOptionPane.ERROR_MESSAGE);
}  


In this way the readability is improved, unnecessary checks are removed as well as casts. 
And it is easier to maintain.