It sounds like you are concerned with both the sodium and fat content of cheese.
Looking first at the sodium issue, mozzarella cheeses can vary quite a bit in sodium content per serving size because of the different amounts of salt used in making the cheeses. Depending on the specific type of mozzarella cheese, a typical range of sodium content can be around 115mg-210mg per ounce (serving size). Of course, sodium is present in just about all parts of a pizza, not only the cheese. As you may know, the recommended daily allowance (RDA) of sodium for an adult male is around 2300mg. That is equivalent to about a teaspoon of salt. However, the FDA and others, including the American Heart Association, have been lobbying for a decrease in the RDA for sodium to around 1500mg (equivalent to about 5/8 teaspoon of salt) even though recent studies are at serious odds with the lowered value for sodium. But, neither the FDA or the AHA is backing off of its 1500mg number. As an aside, I discussed that number with my doctor in a recent routine physical and I mentioned that it would be virtually impossible to meet that number if one ate a typical meal at a restaurant. He agreed and said that one could not eat at a restaurant if he or she was on a low sodium diet.
As for the fat content of mozzarella cheese, for years people were advised to control their input of mozzarella cheese because of the saturated fats. But a very recent study, as discussed, for example, in a recent New York Times article at http://well.blogs.nytimes.com/2014/03/17/study-questions-fat-and-heart-disease-link/
, purports to debunk the long held view implicating saturated fats with heart disease, strokes and other ills. You might also note that so-called "heart healthy" oils like olive oil are not left off the hook. However, there are many other studies that support the use of olive oil as part of a heart healthy diet. For example, olive oil is a key component of the Mediterranean Diet.
So, where does this leave us. First, there are no trans fats in mozzarella cheese, at least at the single serving level. That is a good thing. In fact, if the FDA gets its way, trans fats may well be taken off of the GRAS (generally recognized as safe) list. The comment period on that matter just recently ended.
Second, there is cholesterol in mozzarella cheese so that is something that one might not want to ignore. A typical range for cholesterol for mozzarella cheese is about 15-25mg per one-ounce serving size. People are advised to limit their daily cholesterol input from food sources to about 300mg or about 200mg for those who have high cholesterol. One would need to eat a fair amount of mozzarella cheese to reach that level but it becomes more approachable if one uses meats on a pizza, especially sausage and pepperoni.
Finally, there is the issue of calories, as you noted in the topic heading for your last post. Unless one is judicious in the type of pizza eaten, and the amount eaten, pizza can be quite fattening.