The original PNG transparency test gives a lot more information on the problem
Summary:
Older versions of some big-name programs (Internet Explorer (v6 and older), Adobe Photoshop (v7 and older)) cannot correctly open 32-bit (24-bit color, 8-bit alpha) PNG files with alpha channel transparency. The below image has a yellow background that should be transparent, but is visible in broken programs.
8-bit color with transparency

32-bit color with transparency

How it looks in broken programs

PNG Alpha Test image should look like this:

PNG Alpha Test image looks like this in your browser:

How it looks in broken programs

This PHP code will generate the above image:
<?php
$Image = ImageCreateTrueColor(80, 40);

$back  = ImageColorAllocate($Image, 255, 255, 0);
$red   = ImageColorAllocate($Image, 255,   0, 0);
$green = ImageColorAllocate($Image,   0, 255, 0);
$black = ImageColorAllocate($Image,   0,   0, 0);

ImageColorTransparent($Image, $back);
ImageFilledRectangle($Image, 0, 0, 80, 40, $back);
ImageArc($Image, 20, 20, 32, 32, 120, 0, $red);
ImageString($Image, 5, 20, 20, "hello", $black);

ImagePNG($Image, "c:/bad.png");
?>

The majority of popular image-displaying software had been fixed to work correctly by mid-2004. This is the compatability list according to my latest information (email me if you have any updated compatability information)

8-bit works, 32-bit is broken:Both versions work correctly: