With Juicebox-Lite, the captionPosition is always set to OVERLAY and you will notice that the caption area is always immediately above the thumbnails (at the bottom of the overlay).
What you are noticing is the scaling of the image within the gallery's image area.
Depending on the size and shape of the gallery (which in your case is dependent on the user's browser window), the main image may or may not be scaled so that the bottom of the main image is close to the bottom of the image area.
For example, a landscape image in a portrait-shaped gallery will have space at its top and bottom (resulting in the caption area not overlapping the image).

Make sure that your images are larger than the size at which they will are likely to be displayed in your gallery.
This will ensure that there is not space surrounding all edges of the images in the gallery. (In Juicebox-Lite, large image are scaled down but small images are not scaled up.)

There are certain other things you could do but they would all require Juicebox-Pro.
(1) Set imageScaleMode="FILL" to ensure that the image always fills the image area. (Please note that images will be cropped if their aspect ratio does not match that of the gallery's image area.)
(2) Set captionPosition="OVERLAY_IMAGE" to ensure that the caption area is always overlaid at the bottom of the main images.
(3) Set captionPosition="BELOW_IMAGE" to ensure that the caption area is always displayed below the main images.

Unfortunately, I do not know what might have caused your JuiceboxBuilder-Pro installation to do this but please try the following. (Another user who has reported a similar scenario claims to have had success with this procedure.)

(1) Uninstall JuiceboxBuilder-Pro.
(2) Delete the following folder manually: /Users/your_username/Library/Application Support/Adobe/AIR/ELS/JuiceboxBuilder-Pro/
(3) Search the hard drive for all instances (files or folders) 'JuiceboxBuilder-Pro' and delete whatever is found.
(4) Reinstall JuiceboxBuilder-Pro but to a location other than the application folder.

An image which is currently selected does not have its corresponding thumbnail link disabled.
If an image is requested, then the link will naturally lead to the location of the image on the web server. However, depending of the value of the imagePreloading configuration option, your browser may have the image cached.

Try the following.
Create a sample gallery with large images (large enough to have a significant and noticeable loading time, for example several MB each) and configure it so that the gallery has at least two thumbnail pages.
Set imagePreloading="PAGE".
Upload the gallery to your web server, load the gallery in a browser and go to the first image on the second thumbnail page.
You should notice that the image takes a long time to load.
Now select the next image (on the same thumbnail page) and then select the first image on the second thumbnail page again.
You should notice that the image appears instantly this time (rather than being loaded from scratch).

I hope this makes sense.

Please post suggestions for future versions in the Feature Requests forum thread.
It keeps them all together and ensures that they are not overlooked.
Thank you.

Thank you for reporting this bug.
I have logged a bug report with the developers.
Unfortunately, I do not think there is a workaround at the moment to achieve the same result that setting autoPlayThumbs="FALSE" would give.
However, the bug should hopefully be fixed in the next version of Juicebox-Pro.

Does there seem to be any pattern with regard to how or when JuiceboxBuilder-Pro fails?
Does it happen only when trying to process certain file types or images from a specific source or images with certain file sizes or images with non-standard characters in their filenames?

I have not been able to replicate this problem but if you find out the cause (whether it is a corrupt image or a sequence of events which triggers it), please let me know so that I can investigate further.

WP-Juicebox was not designed to work in a WordPress Multisite environment.
If you post the URL to the web page containing your gallery (which displays the "Juicebox Gallery Id 7 has been deleted.". message), I may be able to determine the cause of the problem and perhaps suggest a solution.
Otherwise, you might like to try manually embedding Juicebox galleries in your WordPress pages or posts using the baseUrl method as documented here.

As you are probably aware, it is not possible to change a configuration option once a gallery has been loaded.
However, you could reload the Juicebox gallery on your page with different settings (using links and a JavaScript function).
Here is an example with buttons to change the gallery's background to either black or white. (It also remembers which image was currently being displayed when a background color change is initiated and displays this image when the gallery is reloaded.)
Create a sample gallery with JuiceboxBuilder-Pro and replace the gallery's 'index.html' page with the the following code:

<!DOCTYPE html>
<html lang="en">
    <head>
        <meta charset="utf-8" />
        <meta name="apple-mobile-web-app-capable" content="yes" />
        <style type="text/css">
            body {
                margin: 0px;
            }
        </style>
        <script type="text/javascript" src="jbcore/juicebox.js"></script>
        <script type="text/javascript">
            var index = 1, jb;
            function loadGallery(bc, fii) {
                jb = new juicebox({
                    backgroundColor: bc,
                    containerId: 'juicebox-container',
                    firstImageIndex: fii,
                    galleryHeight: '400',
                    galleryWidth: '600'
                });
            }
            $(document).ready(function() {
                $('#black').click(function() {
                    loadGallery('#000000', jb.getImageIndex());
                });
                $('#white').click(function() {
                    index = jb.getImageIndex();
                    loadGallery('#ffffff', jb.getImageIndex());
                });
                loadGallery('#000000');
            });
        </script>
        <title>Test</title>
    </head>
    <body>
        <div id="links">
            <input type="button" id="black" value="Black Background Color">
            <span>&nbsp;</span>
            <input type="button" id="white" value="White Background Color">
        </div>
        <div id="juicebox-container"></div>
    </body>
</html>

I'm not exactly sure what you mean by this. Would you want the gallery to be displayed in the theme's header or a sidebar? Either way, to create a widget to do this would probably involve a lot of work. Also, are you suggesting that the gallery pulls in a random image from the Media Library? That in itself would not be too much of a problem (though knowledge of the WordPress API would be required).
There is already a Juicebox plugin for WordPress (WP-Juicebox) but this embeds a Juicebox gallery as the main feature in a page or post and you would need to specify the images that you would like to be displayed (although you could set randomizeImages="TRUE" in the Pro Options text area).

As far as I am aware, there are no plans to integrate any other online photo service.
You could, however, pull in and display images from a custom data source (such as a Picasa Web Album, for example) by using a server-side script to dynamically construct an XML file on-the-fly (as long as your custom data source allows you to fetch the image URLs through an API).
Please see this FAQ:
Can Juicebox handle a custom data source, for example RSS or Instagram?

Unfortunately, I do not have an explanation, either.
However, I am glad that the problem seems to have been resolved (at least for the time being).
If you find out any more about the problem or continue to experience difficulties, please post back to let me know.
Thank you.

If you have already tried uninstalling JuiceboxBuilder-Pro, deleting the folder from my post above (to ensure that no files are left behind) and then reinstalling JuiceboxBuilder-Pro, then there is no reason that I can think of why JuiceboxBuilder-Pro should not function correctly. (It should function just as it did when you first installed it.)
Also, it is possible to install JuiceboxBuilder-Pro alongside JuiceboxBuilder-Lite (and svBuilder and svBuilder-Pro) so there should be no need to uninstall the other applications.

Perhaps you have an anti-virus or other security program installed which is somehow interfering with the functionality of JuiceboxBuilder-Pro. Try making an exception in your security program for JuiceboxBuilder-Pro to see if this helps.

Also, make sure that you are using the current version of Adobe AIR (v4.0) which can be downloaded from here.

Juicebox will use the 'full.html' page for an expanded gallery if expandInNewPage="TRUE" or if the gallery is displayed on an iOS device and the viewport is not locked. Please see here for details.