The ingredient to watch out for in Japanese food (especially authentic Japanese food) are the bonito shavings which are steeped and strained to make the ubiquitous 'dashi' stock.

Omelettes generally have dashi in them. So does the miso soup. The dipping sauces for soba, udon noodles and tempura are made with dashi and tofu is often cooked with it. It's common to find bonito dashi being used even in restaurants in Japan serving vegetarian temple food.

On the plus side, English Japanese restaurants tend to be aware of vegetarians' requirements, so if the establishment label their own food with a 'V' it's likely they've made a vegan 'dashi', perhaps flavoured with shitake as well as the konbu kelp. Japanese food on the whole isn't particularly vegetarian friendly. However, with very little effort, many dishes potentially can be. The trick will be working out if the restaurant actually made that little bit of extra effort.