I'm going to be the odd one and say that you cannot eat sushi. Although the end product looks simple, there is a plethora of ingredients in sushi. On top of this, the cheaper you go or the further away you are from a source of seafood, the more ingredients are used in order to compensate for the lack of flavour in fish that isn't fresh.
I have been living in Japan for the past two and a half years in a region renowned for its seafood and, subsequently, its sushi and sashimi. Unfortunately after being sick for months I did some research into sushi and found out that most of it is not gluten free.
Nori (seaweed) is usually flavoured. This is typically with MSG. Although MSG is gluten free in North America (bacterial fermentation), in Japan and China MSG is sometimes still derived from gluten. If your chef is using nori imported from either of these countries, it may not be safe. Unfortunately MSG is rarely labelled as MSG and is therefore hard to spot.
Su (rice vinegar) also contains wheat at times.
I have been off sushi for about 3 months now and, as hard as it is, I have never felt better.
Do not assume that if you can find gluten free rice vinegar in your supermarket, it means your local sushi chef is using something similar. Chefs will often use imported items that do not contain the same ingredients.