Disclaimer: I am a relatively new spinner with very limited experience dealing with raw fleece. I've been asked to show the process I use, and some of the things to look for when sorting through a newly shorn fleece. I am not qualified to make judgements on the quality (or lack thereof) of a fleece. This fleece was free and from a sheep not raised for it's wool --- if that tells you anything.
The first thing I do is to lay the fleece out "whole" if possible. The shearers seem to try to keep the fleece in more or less one piece so if you are careful and don't tug it to bits, you can usually lay it out and push it into the basic shape it was when it came off the sheep's back.
I find it helpful to do this because you can then sort out general areas to look for problems. For instance, around the outer edges are where you will find the wool that was at the bum end, the underbelly and legs and around the neck and face.
The bum end of course is where you will find "dags" as the New Zealander's call them. This is the dried bits of sheep poop. Never fear, although it is smelly and unpleasant it does wash out.
New Zealander's have a saying "Rattle yer dags". It means to hurry up. It comes from the rattling sound that the clumps of dried poop make as the dangling bits bang together when the sheep are hurrying along.
Another thing to keep an eye out for is VM (vegetable matter --- bits of grass, thorn and feed). You can see large bits of it in the above picture.
The yellow crud is "yolk", something like sheep sweat. It is seen close to the skin of the animal. Although it washes out it can stain the wool if it is particularly bad. In the above picture the yolk is visible along the bottom edge. The dark bits at the other end of the locks are weathering. This is dirt and sometimes sun damage that forms on the outside of the sheep's coat. Sheep that are raised specifically for handspinners sometimes wear a coat to prevent this.
After looking at the top side of the fleece I turn it over and look close at the cut side for short bits called "second cuts". These shorter bits are the result of a shearer going over the same area more than once. The short bits of fiber, if left in and carded, will result in noil in the batts or rolags. Noil makes your yarn lumpy and sometimes weaker.
The pictures above and below show an example of how second cuts look on the underside of the fleece. In the picture above, the second cut stands out( in the centre of the picture) like a little cotton ball floating above the locks.
This final photo shows the dreaded VM. In this particular section it is quite fine and spread thoroughly through the fleece from tips to cut ends. I suspect this section may be from the neck of the sheep where it would be exposed to more of the animal's feed. If you are carding your wool this VM is a problem and needs to be removed first or it will be spread throughout your wool. I comb my wool (I don't own carders) and find that most of the VM just falls out into my lap during the process so I don't worry about it too much.
Like I said, I am inexperienced and if you can add more or if I need correcting, please feel free to elaborate in the comment section. Thanks.