The fog lights on the E36 are prone to stone chips because they are so low
on the ground and can also crack due to thermal stress if you go through a puddle
of water when they are hot.
Fortunately they are easy and not too expensive to replace. German & Swedish sell original quality replacements for £30+VAT or alternative ones for £20+VAT.
Pictured below is the drivers side brake duct and fog light. To release the fog light all you need to do is insert a screw driver in the hole at the top and push the releasing clip forwards. The fog light will then pivot on the opposite side and come out.
The picture below shows the release clip on the left and the pivot point on the right of the photo.
If this plastic clip has broken then it is more difficult to remove the fog
light. You need to remove the 4 bolts and 2 plastic rivets holding the plastic
panel underneath to the bumper. You will probably have to force the rivets out
and buy a couple more. They are only about 12p each from a dealer.
Once the panel is off then raise the wheel up a little by for example driving onto a kerb and put your head underneath.
The picture below is what you should be able to see. You will need to hook a flat bit of metal over the top of the bracket and down between the bracket and other side of the lever and then twist it.
The finished result. You might wish to replace the fog light the opposite side aswell as you can see from my photo the old fog light glass discolours after a while.