Hi Johann!
The problem is, that on https websites the mixed contents are blocked, so the http links in your code.
For the Smart Slider it should be enough, if you would go to the Settings, and use the “Translate url” option, where you should write “http:” to the “From”, and “https:” to the “To”.
If you would install Firebug into your Firefox browser, press F12 on this page, click on Console, and refresh the page, then you will see, which contents are still blocked, because there is many other too outside our plugin. Also I can see, that you are using some javascript minification, which is also blocked and I’m not sure, if our code isn’t there too.
The best I can suggest is to save down your website’s files, and use some program, like Notepad++, where you have an option to search and replace texts in files. But first make a backup from these files.
With Notepad++ you can do that, if you would press Ctrl + SHIFT + F, write “http:” to the searchword, “https:” to the replacement, and choose your folder, where all of your files are. It will take a while, so just leave it there.
Then go to your database, export it, and do the same, have a backup, then search and replace your urls. After this you should delete your database, and import this new replaced one. If you feel more comfortable, you won’t need to delete it, just create a new one, and then rewrite the database name in your wp-config.php file.