Wow. This is interesting. I live in an area where farmed salmon is a hugely contentious issue for a variety of reasons. I also work for a marine science organization that has a program to help consumers select more environmentally fish, and teach marine biology as a sideline. I've also worked with different scientists who design fish diets and rear fish for reintroduction, aquaculture, and to study the effects of ocean acidification and rising ocean temperatures.
Most of the issues here are not ones I would think of as a consideration when buying fish. My concerns are primarily environmental.
We are running out of fish and seafood. Full stop. There will be none left if we continue doing what we are doing. This is about as close to a scientific fact as you can get. Given the destruction of marine environments and climate change, we need to find a way to supply the world's population with the seafood it needs. For that, we need to invest in aquaculture research.
Some aquaculture is very environmentally friendly, and some is incredibly damaging. It depends on the organism, and where and how it's farmed. An example from earlier in the thread, tilapia, is a good one in this regard. They're a freshwater fish, usually reared in closed containment systems. You don't have to worry about them spreading out and contaminating local species or carrying pathogens. They're vegetarian, which means you're usually looking at a net gain of protein. Funnily enough, most people who complain about tilapia diets are completely ok with eating prawns and other shrimps, whose diet is just as, if not more nasty, and come along with significant environmental and human rights concerns.
Salmon, on the other hand, tend to be farmed in open water pens. For a variety of reasons, in North America, Atlantic salmon species are being farmed in the Pacific Ocean. There are concerns with parasites (specifically sea lice), disease, and when these salmon escape they are competing with local species for food and disrupting spawning. Lights use to increase growth attract local species which then become easy prey, both for naturally occurring predators and the farmed salmon (again, open nets are being used.) Salmon farmers are allowed to kill nuisance species which include marine mammals (this isn't including animals who just get caught in the net and die.) Algae blooms are another problem with disrupt the local ecology. Then there's the actual net loss of protein. Because salmon are carnivores, they're fed fish pellets made up of other ocean species of fish, so you're not actually "producing" fish protein at all. There have been some advances in soy based formulas, but they're aren't great yet. If you could fix that and move to inland closed containment systems, it would be much more viable. Personally, I have no issues with the GMO feed or dye used to colour the flesh. Both are recognized as generally safe in the scientific community.
There are a lot of very good options out there for seafood. And there are some very bad options, whether you're talking about health concerns (for example, mercury levels in pelagic predators like tuna), environmental (sharks, orange roughie, chilean seabass), or human rights.