Non-meat and non-dairy vegetarians--also called vegans--might have a problem getting enough Vitamin B-12 because this is found almost exclusively in animal products. They should look for products fortified with this vitamin; some soy milks, for example, are fortified with B-12 and other nutrients.
Lacto-ovo vegetarians, who drink milk and eat eggs, probably will not have this problem because those products are rich in B-12.
Vegetarians also should keep in mind that their diets tend to be high in fiber, which generally is a positive, healthy thing. But fiber does tend to interfere with the absorption of calcium, iron and zinc, so extra amounts of those minerals might be advisable to make sure enough is being absorbed.
One problem for vegetarians is that the iron from meat, fish and chicken is better absorbed than the iron from plant foods. Iron absorption can be boosted, however, by including foods high in Vitamin C. To do that, look for recipes that include sources of both those nutrients. An example would be brown rice, tofu or lentils (all iron-rich foods) with a sauce or salad made with peppers, tomatoes, oranges or other Vitamin-C sources.