Well I didn't look at it long enough to determine the problem, but I can tell you that it appears to be javascript based, and your problems may be related to that script.
It also appears to be acting differently in different browsers- little side note, when I visited with Chrome a little note popped up at the top notifying me that my browser was not supported, and it encouraged me to switch to a list of different browsers, but chrome was on the suggested list.
Looking at the missing images, the src for one that displays fine is this:
http://www.anewagephoenix.com/skin/smart_template/custom/js/social/images/16/Yahoo.gif
Here is the src of one that is missing:
http://www.anewagephoenix.com/skin/smart_template/custom/js/social/images/16/Google.gif
I wonder if the file is on the server or not? I would check in that directory and see if the image exists.