There is a lot going on within your web page and as it loads, you can visibly see elements shifting around until they settle in place (as the JavaScript and CSS is being rendered by the browser).
There are differences in your web page, not just between versions of Internet Explorer but also between different browsers.
For example, in Firefox 19.0.2, your 'Select Language' combobox is initially completely obscured by the gallery (which it is not in IE10, Chrome 25 or Safari 5.1.7) but it partially appears if you resize the browser window and then maximize it.
As you are expressing your galleryWidth and galleryHeight as percentages, check all parent containers of the Juicebox container (your 'box_slideshow' <div>) to ensure that they all have heights specified via CSS and please see the Using Percentage Heights note in the embedding guide. This suggests using inline CSS on the parent containers rather than on the Juicebox container (your 'box_slideshow' <div>) itself.
If there is a problem with the gallery not being able to determine it's height in certain browsers, then you could perhaps express your gallery's height as a fixed pixel value rather than as a percentage.
Another workaround might be to isolate the gallery completely from the rest of your web page by embedding it using an <iframe>, documented as Option #2 here. As your gallery does not use the Expand Button or Back Button, there should be no drawbacks to using an <iframe>. This should avoid any conflicts with your main page and should hopefully work in all browsers.