Internet Explorer doesn't handle transparent PNGs well. Up until about now I wasn't aware though that there can be problems with other Internet Explorer versions as well. I discovered that my transparent PNGs had a huge black border for no apparent reason.
Obviously that's jquery's fault - as soon as you work with the hide/show functions, this particular phenomenon can happen. So far I didn't find the time to carefully look up my problem and maybe find a better, more elegant solution. So far I solved the problem by saving the images in question as jpg or PNG in 8-bit mode. Or, if none of that helps, I found alternatives to the jquery functions.