OK, this is somehow related NOT to your code, but to image size. (I am humiliated.)
This is what I did:
1. Deleted all of the images I had been using.
2. Created an image of exactly 940pixels by 420 pixels and saved the same image three times as slide1.gif, slide1.png and slide1.jpg.
3. Uploaded all of them to my server.
4. Linked to each of them in the front page slider.
5. Browsed to my front page. No red border appeared.
I was sure that I had correctly sized all the images I had been using, but I must have made a mistake in one or two of them. The front page slider is working now in Firefox, Internet Explorer and in Chrome.
Sigh... As Albert Einstein famously said, "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."