A few thoughts:
One of the reasons cats are mandatory carnivores is because they must have pre-formed Vitamin A, as they can not convert beta-carotene into Vitamin A. Liver is a great source of Vitamin A but should not be fed exclusively like any raw meat for two reasons: 1) the potential for excessive Vitamin A called Hypervitaminosis A and, as with all meats (not just livers) a tendency to induce a calcium deficiency which then requires supplementation to overcome it (if you don't stop doing it, or your cat refuses to eat anything else). For Hypervitaminosis A, I must make clear, there has to be quite a history of exclusive feeding on liver, so 2 - 3 meals a week should be OK, just not every day otherwise it can and will happen. (If you think what happens in the wild, no cat just eats the organ meats of an animal it kills, it eats fur and ears and all parts, indeed big cats often eat the intestines of bovines with grass in the stomach too (known as 'green tripe' in the food trade and very nutritious) - and yes, domesticated cats may leave the rest of a mouse but generally this is because they're already well fed or are 'topping' up on a deficiency.
As a previous contributor has said, cats need a diet with high protein content, and this is because they can not conserve nitrogen and thus protein (consisting of amino acids, compounds containing nitrogen) alone must be used to provide energy rather than like dogs, or humans for that matter, who can get energy from both carbs and fats exclusively if needs be (not good long term of course).
Cats need fats however and fish is one of the best sources as long again as it's not an exclusive feed or your cat may get fatty diarrhoea from too much unsaturated fat, so combine with some saturated animal fat, dairy if they can tolerate it or fish oils including small amounts of fish liver oils, again everything in moderation and balance.
Cats can utilise both iron and copper from meats but the loss of coat colour could mean either an excess or lack (bioavailability) of copper depending on the meat used as iron and copper fight for absorption and iron would be the most bioavailable in red meat probably pushing out copper. How the cattle are fed, if you're feeding beef for example, will affect the minerals in the meat never mind the use of sick and 'downer' animals, often highly deficient, in this regard. Whilst such animals aren't allowed into the human food chain (supposedly) cattle fed grain in food lots are.....with corresponding negative effects on the human food chain, but that's another story. Alternately for coats lacking lustre consider calcium deficiency as above as this shows initial signs in the coat (lack of lustre and falling out) before the more serious effects become apparent. But then, the more I think about it, so does quite a few other deficiencies so nothing completely conclusive to add there, but calcium deficiency is a well-known problem with cats fed exclusively on red meat.
According to my faithful Hungerfords's Diseases of Livestock which, for some reason also includes cats, "Generally commercial canned or dry foods with two or three varied organ meats (kidney, heart, liver), occasional cheese, cooked fish, meat, baby foods, yoghurt, cooked vegetables and cereals, two egg yolks per week and a daily teaspoonful of cooking oil, bacon fat or butter, all used with discretion, are general guides."
That's the sort of combo my cats did very well on years ago before the 'tin din' era.
Finally, many years ago now, I visited a homeopathic vet with my dogs who were in dire straits with 'genetic' problems (bilateral stiffness of front legs) and he pulled them off all cereal-based foods and put them on a little goats milk, green tripe, tinned fish (like pilchards, which they loved the best), rabbit, organic chicken, vegetables (no solanacea like potatoes), brown rice, brewers yeast, cod liver oil and all their significant problems cleared up within weeks and they became like puppies again instead of old crocks at 5 years. I thought until then I had them on the best red meat and biscuits diet, never 'tin din', but in my ignorance had contributed to their problems. We live and learn.
So, as always, even with the peculiar dietary likes of cats, it would seem varied and balanced is the way to go. Sometimes that even works for humans too.:D
Kind regards
Sheila