Transparent/Diffuse draw error

Im getting a strange drawing result when I use the Transparent/Diffuse shader. Below you will see it compared to the Transparent/Cutout - Diffuse shader, which renders correctly.

The transparent edges are a bit too hard for me, so I would like to use the Transparent/Diffuse one, but it doesn’t display correctly.

Why is this happening? Ive used the Transparent/Diffuse shader before but it didn’t render like this.

Edit: This is what the Transparent/VertexLit shader looks like.

You can’t use that shader on a whole object like that. You never know which faces are going to be drawn first. This illustrates the problem but isn’t pixel-lit.