Assuming the fish is prepared properly and is sushi grade, how many times per week can I eat sushi without having to worry about mercury poisoning and/or health concerns? I'm not sure if the kind of fish is important, but I generally eat salmon, white tuna, and yellowtail.
Provided you go to a reputable sushi restaurant with good hygiene standards, you should have no problem in terms of bacteria or parasite-related health problems. Most fish used in sushi restaurants is flash-frozen at -20 degrees C (-4F), which kills parasites outright.
As for mercury, you can check the FDA's page detailing the amount of mercury in the various species of edible fish, to help you make an informed decision. They recommend that higher risk groups, such as pregnant women, limit their intake of certain fish to 12oz/week.
Generally, sushi is extremely healthy as it is low in fat and high in vitamins and minerals - Japan has the highest life expectancy in the world, after all: diet plays a big part in that.
Salmon are generally riddled with parasites, so if you purchase raw salmon, only use it if you know it has been frozen in accordance with FDA guidelines, which means it was previously frozen at a low enough temperature (lower than you can get in your home appliances) for long enough to kill the worms. Fresh off the boat? Cook the salmon.
Tuna and yellowtail (Japanese amberjack) are generally not a parasite risk, but if you live on the east coast and they call their local species of amberjack "yellowtail," it is a different species that often has worms, though, to my knowledge, it is not harmful to humans (but why risk it?).
The thing about delicious large ocean fish is that they are almost all predators, which means mercury will concentrate in them. A lot of "how much" will depend on local human influence and how far a species of fish ranges. I would imagine east coast/Atlantic US fish, with a lot of the traditional coal-fired power generation, is going to have more mercury issues. It's best to check with your local state agencies, which will have advisories for which types of fish present mercury risks and at what amounts (larger fish size will have more) and how often the fish can be safely consumed, if at all.