The only one you're going to get for sure is B12 as vegan, and probably not enough as vegetarian or omni.
Personally I tend to be a little light on K and calcium because I don't eat as many dark leafy greens as I should. Of course I had the same problem as an omni as well(infact I was not meeting my needs of many things). I haven't noticed vegans having problems any more than vegetarians or omnis.
I think a lot of it is that nobody thinks about an omni diet. It's only when you change it you start to wonder.
Oh one thing to watch for that is not a deficiency but is still important is maintaining a good omega3:6 ratio. 1:4 is the ratio is that has been decided to be good for reasons I have no idea about, if there are reasons at all.....pretty much though from what I understand a 1:1 ratio would be better but they probably say 1:4 to make it seem obtainable much like the food guide.
Anyways vegans more often have bad ratios, vegetarians are the next worst, and omnis are the least bad.
The best places to read about these topics are these websites from vegan registered dietitians: www.veganhealth.org and www.theveganrd.com. B12 supplementation is definitely a requirement. Other nutrients to pay attention to are iron (especially for women who menstruate), calcium, vitamin D and iodine (if you don't use iodized salt). Protein is often a concern, but it is easy to get enough as long as you eat legumes or soy foods.
Kaiser Permanente (one of the largest health insurance companies in the United States) recommends plant-based vegan diets for the treatment of obesity, diabetes, heart disease, and hypertension. Kaiser Permanente has published a vegan nutrition guide - it explains the nutrients that vegans should focus on: http://www.kphealthyme.com/Healthy-E...ased-Diet.aspx
“Specific recommendations for a healthy diet include: eating more fruit, vegetables, legumes, nuts and grains; cutting down on salt, sugar and fats. It is also advisable to choose unsaturated fats, instead of saturated fats and towards the elimination of trans-fatty acids."
- United Nations' World Health Organization