Which leads me to fat. It has such a bad reputation these days, why should we eat any? Well, first, fat acts a kind of slow burning fuel for the body, so a little helps give you more energy. Second, many nutrients can't be used properly in the absence of fat, and it's not clear whether stored fat works nearly as well (or at all) for that purpose. In other words, if you don't have a little fat with your meal, you might as well not have eaten the calcium and vitamins A, D, and E, as well as other fat-soluble nutrients.
If you're worried about heart disease, replace animal fats with vegetable fats. If you're worried about calories, just make sure you include at least a little with every meal. Keep in mind that removing all fat from the diet can actually cause you to gain weight (an odd but true fact). Vitamin E not only needs fat to be digested, it's almost impossible to get it at all from non-fat sources. Keep in mind that most breads include a little fat, and there are unusual sources like avocados.
I would suggest avoiding hydrogenated fats such as those in shelf-stable peanut butter and in margarine. I think in recent years these have been connected to several health problems themselves. I use the kind of peanut butter that's just ground peanuts and has to be refrigerated after opening. More expensive, but no hydrogenated fats, and the taste is SO much better.