The other nutrients that may be missing in a vegetarian diet are iron and zinc. Iron can be a little tricky, since it's harder to absorb from non-animal sources and some vegetarian staples can actually block your body from accepting it. You'll have to eat a little more than an omnivore, but I promise it's not that hard.
I don't pay any attention at all to where my iron comes from, I don't eat anything fortified with iron, and yet every time I give blood the phlebotomist complements me on having one of the best iron levels s/he has seen all day. If you do have problems with it though, try upping the ante with whole grains and dark leafy greens, and remember that eating vitamin C with iron makes it easier for your body to absorb the mineral.
Zinc is the other mineral that you may have to pay particular attention to. Again, I don't bother scouring my pantry for sources of zinc, but I get enough anyway. Zinc can generally be found in your protein foods--nuts, seeds, beans, whole grains, etc. If you ever think you won't meet your daily requirement, grab a handful of pumpkin seeds or dip some pita chips in hummus.
A diet that is completely plant based (a.k.a. a vegan diet) may also be lacking in calcium. Since many vegans and vegetarians pay special attention to getting adequate amounts of protein, they sometimes eat more than the recommended daily allowance, which can damage the body's ability to absorb calcium. Salt has the same effect, but to a greater extent. So if you find yourself eating a lot of protein or sodium, try to consume just a little more than the recommended 1000mg of calcium a day.
Although dairy is touted as being the star of the calcium scene (Got Milk?) there are numerous, dairy-free options for vegans out there. Soy* is particularly high in calcium, as is black strap molasses (although that's a bit more difficult to integrate into the diet.) Dark, leafy greens such as bok choy, broccoli, collard greens, Chinese cabbage, kale, mustard greens, and okra are also key sources.
In the same way that sodium and protein demote calcium absorption, Vitamin D consumption promotes it. This is a vitamin that's naturally found in very few foods, vegan or otherwise. Luckily, the human body can create its own Vitamin D through just a few minutes of sun exposure every day. There are certain mushrooms that provide significant amounts of Vitamin D, but other than that the only real way to obtain it through the diet is to eat fortified foods.
*A note on soy: Unfermented soy foods do contain a compound known as phytoestrogen. It's a plant estrogen, very different from human estrogen, and is completely harmless unless consumed in excess. Unfortunately "in excess" is a pretty easy amount to consume if you're relying on soy as your main source of protein and/or calcium.
The best way to avoid any negative side effects are to simply enjoy soy in moderation. Choose rice, nut, coconut, or hemp milks over soy milk, and choose fermented soy products (such as tempeh) over unfermented soy products (such as tofu.) It's fine to have unfermented soy products every once in a while, but it's important not to overdo it.