Take this with a grain of salt since I’m no coder: But basically premultiply will multiply the colors of the texture with what I presume is the alpha channel before blending it to the background. For example, if you have a 100 % green texture with a 10 % alpha, it multiplies them so that the green color is changed to 10 % green, and that gives more smoother blending.
However, on the other hand straight alpha blending will not touch the colors of the texture, and go ahead to blend a 100 % green color with an alpha of 10 %, which will result in aliasing-looking artifacts within the texture since the colors of the in-between areas between 100 % alpha (fully opaque) to 0 % alpha (fully transparent) is not smoothed.
Your texture had mostly partially transparent pixels, and combined with the gamma correction of Blender 2.5’s made a before slight error to be so pronounced. Since most textures with alpha is used to add colors, it’s a nice habit to check the premultiply button whenever you work with textures that have an alpha channel. The cases where you’d want to preserve the original transparent color (such as when adding a alpha mapped glow effect) are so rare in texturing that you don’t have to worry about them. Those issues usually don’t arise until you sit in the compositor with three or four render layers that you need to combine…
I’ve had a lot of pain with alpha mapped render layers, for instance in my Phage T4 render, the viruses themselves had a defocus node applied on their own render layer. This also blurred the alpha channel, and when I tried to blend it back with premultiply, their thin feet were almost gone, so I had to use a semi-method of straight alpha and premultiply to find a balance between blobby alpha transition and visibility of the feet. The results weren’t perfect but for the style of render the artifacts were almost unnoticeable, and that was good enough for me.
To summarize, it’s probably a good idea to always use the premultiply option when working with alpha-mapped textures. 
