First of all, please try upgrading your Juicebox-Pro gallery from v1.1.1 to the current version (v1.2.0) by following the instructions here as many bugs have been fixed since v1.1.1. Please see the Juicebox - Version History for a full list of changes.

Also, try validating your web page with the W3C Markup Validation Service and fix the errors reported.
Once your web page validates correctly, it should be rendered with greater predictability and consistency across different browsers.

In order for a Juicebox gallery to function correctly, all the files (including the HTML document containing the JavaScript embedding code) must be on the same domain or subdomain (www.mydomain.com is a subdomain of domain.com).
This is due to the JavaScript same-origin policy security restriction. Please see this web page for more information.

To have the gallery display when visiting both www.mydomain.com and domain.com, try using relative paths (rather than absolute paths which hardcode either www.mydomain.com or domain.com) in your embedding code.

You can set a gallery's dimensions to absolute pixel values (rather than percentages) with embedding code such as:

<!--START JUICEBOX EMBED-->
<script src="jbcore/juicebox.js"></script>
<script>
new juicebox({
containerId : "juicebox-container",
galleryWidth: "920",
galleryHeight: "920",
backgroundColor: "#222222"
});
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

When doing so, your gallery will always be a fixed size, regardless of the size of the user's browser window.
If creating or editing your gallery with JuiceboxBuilder-Pro, you can set the gallery's dimensions in the 'Customize -> Lite' section.

When embedding your gallery with Adobe Muse (following the instructions here), you must set your gallery's height (to an absolute pixel value) in the gallery's own embedding code.
You can leave the gallery's width at 100% and then constrain the gallery to a fixed width using the width of the HTML frame in Adobe Muse.

Try validating your web page with the W3C Markup Validation Service to see if there are any HTML errors on the page which may be contributing to the problem.
Also, make sure that your web host does not have hotlink protection enabled on your hosting account and that all your gallery files are on the same domain.
If you continue to experience difficulties, please post the URL to your gallery so that I can take a look at it live.

Thank you for the additional information.
I can find very little information about this theme on the internet other than this forum post.
I cannot confirm whether the information in the post is correct but it would appear that the theme is known to conflict with at least one other plugin, includes about 30 JavaScript files and allegedly contains 'a lot of JavaScript errors'. If any of this is true, then it may be very hard to debug and the only solution may be to switch themes whilst creating your WP-Juicebox galleries.
However, the WP-Juicebox 'Add Gallery' pop-up window is essentially a self-contained web page and should not conflict with any JavaScript files loaded in the standard admin section pages.

I have emailed you with an address where you can send me login details to your WordPress Dashboard.
I will gladly take a look but please be aware that I cannot be sure that I will be able to either diagnose or fix the problem.

Unfortunately, the theme you use is not free so I am unable to try this for myself.
Is the error message displayed on-screen when you initially try to view a gallery (or at some other point, such as trying to go fullscreen)?
Are you able to try on a different web server to see if this makes any difference?

@jhob

Introducing a cross fade transition is on the roadmap and should hopefully be included in a future version of Juicebox-Pro (although I do not know when this may be).

This embedding code will display one image (via CSS) as a background to the gallery when the thumbnails are displayed and a different image when the thumbnails are hidden. In order for the background to be visible, the gallery's own background must be transparent.

<!--START JUICEBOX EMBED-->
<script src="jbcore/juicebox.js"></script>
<script>
    jb = new juicebox({
        containerId: 'juicebox-container',
        backgroundColor: 'rgba(0,0,0,0)'
    });
    
    jb.onShowThumbs = function(isShowing) {
        var element = document.getElementById('juicebox-container');
        var image;
        if (isShowing) {
            image = 'image1.jpg';
        } else {
            image = 'image2.jpg';
        }
        element.style.backgroundImage="url('" + image + "')";
    };
</script>
<div id="juicebox-container" style="background-image: url('image1.jpg');"></div>
<!--END JUICEBOX EMBED-->

On the 'Manage Galleries' page, WP-Juicebox lists all XML files that it finds in the 'wp-content/uploads/juicebox/' folder. If there are more galleries than will fit in your browser window, you shjould be able to scroll down to see the rest.
Take a look in the 'wp-content/uploads/juicebox/' folder to check that there are, indeed, 274 XML files.
Also, if you have manually edited any of the XML files, make sure that when you resave them, you use a lowercase '.xml' file extension.

You could perhaps use the Juicebox-Pro API, specifically the onShowThumbs() event, to change the background of your gallery depending on whether or not the thumbnails are displayed.
The online demo notes in the 'API Output' text area when the thumbnails are displayed or hidden. You could view the source of the page in your browser and modify it to suit your own needs. Please note that knowledge of JavaScript will be required.

You could perhaps try adding CSS such as the following to the end of the 'jbcore/classic/theme.css' file (though please note that this is untested and I do not know if it will work or will have any unwanted knock-on effects).

.jb-splash-holder img {
    left: 0px !important;
    top: 0px !important;
}

The text is currently hardcoded into the 'juicebox.js' file (which is packed and obfuscated and cannot be modified).

However, the ability for a user to enter custom text for the on-screen tooltip text and messages (similar to the SimpleViewer languageList configuration option) is on the roadmap and will hopefully be introduced in a future version of Juicebox-Pro (although I do not know when this may be).