Mipmapping causes some block faces to become too dark

Grass blocks (in the default texturepack and in other texturepacks - i checked!) on the side of the screen and a bit away from from the player seem to have a small black overlay, seemingly a texture glitch. This can be seen on the attached picture.

This also affects other blocks like leaves.

This doesn't happen if mipmapping is disabled, and higher levels of mipmapping make the issue more severe.