Everyone is at risk of having nutritional deficiencies if they don't eat "a proper balance of foods".
Vegans (aka strict vegetarians), in general, are more at risk for a few particular nutritional deficiencies, depending on how they eat. One thing that is true for all vegans is they need to find a reliable source of vitamin B12 since that's not available in any non-fortified/non-supplemented vegan diet.
Generally speaking, vegans and vegetarians should pay a little extra attention to make sure they get things like calcium protein, iron, omega 3s, and of course B12. That's not usually a problem for someone who eats plenty of a wide variety of plant foods (both cooked and raw, some fortified, and definately some legumes).
And generally speaking, non-veg folks should pay a little extra attention to ensure they get enough fiber, beta-carotene, vitamin C, and not too much cholesterol. That's often a problem for anyone eating the Standard American Diet (most Americans don't eat enough fruits and veggies), but it's not a problem for anyone who eats "mostly plants."
And everyone needs to find a good source of vitamin D. Luckily, it's been added to most milks, dairy and non, so anyone who regularly consumes fortified milks (cow's milk, soy milk, almond milk) should be OK on that front.