Wierd borders on edges of alpha texture.

I’m having an issue with alpha textures in the opengl-render, at first I thought it was an issue with the material/texture, but then I found out a transparent material that works on one object, breaks on another!

More details are in the linked image.

This is the classic alpha sorting problem that has plagued all video games since forever.
The easiest solution is to merge the 2 textures in an image editor beforehand.
And try to prevent semi-transparent textures from ever overlapping.

You may try another way to render the transparency, maybe a clip map would work best? This may help you: http://www.katsbits.com/tutorials/blender/scene-view-alpha-transparency.php