A possible lack of Vitamin B12 is an issue always mentioned. It can cause anemia, but only in the long run. As with every nutritional strategy or diet you can 'do it wrong' and this does not exclude a vegetarian or vegan diet.
To be save, you might use some VB12-supplements here, although it should be said that generally in your liver you have a high storage amount that may last for years before you get negative effects. Also, make sure you eat lots of different fruits, veggies during the day in order to maintain essential nutritional diversity. Also, many starting vegetarians make the mistake to eat too many dairy products then as a replacement. This is not recommendable at all.