Teeth like the carnassial pair would not be necessaria in herbivores, because of their vegetarian diet. Herbivores, have little use or need for slicing and tearing. Perhaps the second most important way of identifying mammal is by the skin and fur. The skin of a mammal contains sweat glands to help cool off the animal, and for dealing with cold stress, a mammal has fur to keep itself warm. Besides sweat glands, a mammal's skin also contains mammary glands.
Mammary glands are actually modified sweat glands which produce milk.
Another important gland in the skin, is what is called the sebaceous gland. These glands release oils which protect the mammal's fur and hair. This serves multiple purposes. One effect of this is it makes the animal look larger than it really is. Another reason for the erector muscles, is when the hair stands on end, it provides for better insulation.