Desalination Brine Disposal

I assume it's about the salt that is dumped back into the ocean after removing the water from it.

Yes. So it is not an issue for the device. However, the salt does end up back in the ocean where at scale the salt levels will be higher leading to the (edit: local) environmental issues mentioned by the GP.

Straight up dumping it in the ocean is generally considered bad. The standard trick is to wash/mix the brine with fresh ocean water to reduce the concentration of salt before dumping it back. Another interesting byproduct that is often overlooked are the metals and minerals. Things like lithium (and even gold) are relatively abundant in sea water and could be recovered from the brine (at the cost of complexity of course).

Where does the salt go when you desalinate? At a large enough scale, would we risk salting some area (or body of water) to death?

It probably wouldn't. Desalinization leaves a lot of salty brine to be disposed of.

With anything involving seawater, you'll run into the same issues as any desalination plant - where to put the enormous amounts of brine? Potable water is bad enough to electrolyze as there are lots of minerals in it, but salt water is a whole lot worse - and there are massive concerns about the toxicity of brine.

My thinking is that if you dump brine into the sea you're a putting in a liquid that marine life can swim though and be harmed by. Another problem is just how to get the byproducts of desalination away from the plant.If the salt were made into a boat, it could be sailed away (moved more easily than on land) and could mix with seawater over a much wider area. Even if it sinks after a short period, it would still be in a rock-like form that would mix with seawater over a longer time perio

Dump it on the roads in the North during the winter.Or, more seriously, if it is salt that was extracted from the sea, there shouldn't be much harm in putting it back. The fresh water that was extracted will end up back in the sea also, so overall there should be no increase in salinity (except locally where the salt is dumped).

Isn't it going to create local ultra salty water?

The salt was in the water to begin with. If you read that reference that you posted, you'll see that the problem is the waste chemicals (not salt), and the increase in temperature of the water. It's plausible that they could filter out the waste chemicals, but I'm not sure about the heat.