I think the main concern about arsenic comes from an extremely high amount of contamination in drinking water. It is probable that we actually need trace amounts of arsenic, as has been demonstrated in the case of some animal studies. We have yet to see a potential depletion in humans, because arsenic is quite ubiquitous in food.
Arsenic is also readily excreted, so the main worry is taking in too much in a short time. And unless your drinking like a bottle of concentrace in a day, I think you'll be okay ;). You would probably have to worry about dehydration from salty water before you have to ever worry about heavy metal poisoning from using sea salt in your water. Unless of course you are using some sort of back alley sea salt. If you are concerned, there are other sources of whole mineral salts, like Real Salt (http://www.realsalt.com/) which I personally enjoy.
Two types of arsenic out there: organic and inorganic. Inorganic is what you'll find in drinking water and salt. It's the bad stuff that can cause toxic reactions. The dose makes the poison, so a tiny amount will likely not cause any health problems. Organic arsenic compounds are what are used in some drugs in livestock. It is relatively non-toxic, and does not convert appreciably to toxic inorganic arsenic.