What Makes Fish Kosher?
The Torah [Vayikra, 11:9] states that Kosher fish have both Snapir (fins) and  Kaskeses (scales). The Rama, [YD, 83:1] explains that  Kaskeses are only those scales that can be easily removed without tearing the skin of the fish. Traditionally, this was tested by tossing the fish in a cloth and inspecting the cloth for scales.

Chazal [Nida 51:] teach that all fish with scales will also have fins [Kreisi U’Pleisi YD 83:3 however explains that this means that most but not necessarily all fish have fins if they have scales. The Taz YD [ibid.:3], and Pri Megadim, Mishbetzos Zahav [ibid.] disagree. According to the Kreisi, we accept unidentifiable fish as Kosher even if we cannot check for fins, and even though this fish may not be Kosher, since the overwhelming majority of fish that have scales do have fins and are Kosher.

The Gemara, Chullin [66:] explains that although all fish with scales have fins, and it would suffice therefore to define Kosher fish simply as those with scales, it nevertheless lists fins as a second Kosher identifying mark, just in order to provide greater opportunity for learning Torah; “LeHagDil Torah”. 

The Rambam [Sefer Hamitzvos, Rambam, Asin 149 - 152] explains that when the Torah says, “This, one shall eat ….” It does not mean that we are commanded to eat but that we are commanded to identify all Kosher species, even if we do not intend to eat them. The Sefer HaChinuch, Mitzvah 153 and 155, understands that the Ramban disagrees. See Darkei Teshuva [83:1] 

Skinless fish fillets, and pieces of meat of fowl, must have their Kosher status verified according to Halachic standards. This means confirmation through a reliable Kosher witness, either a live breathing witness, or the witness' testimony via a Kosher tamper evident seal on a pack. Accordingly, Rav Moshe Feinstein [Shu”t Igros Moshe YD [3:8] and Rav Henkin, Kol Torah, 1964 pg. 29, 1964] rule that tinned fish are not Kosher unless every fish has been checked. See, “The Tell Tail Sign – Star-K World Fish Production” by Rabbi Moshe Heineman. “It is the Star-K policy to require a Mashgiach Temidi who inspects every single fish throughout the entire production of canned tuna.”

The OU however disagrees. “OU endorses buying skinless salmon without sealed Kosher certification. So long as the consumer is familiar with what salmon is supposed to look like, we are not concerned that a non-Kosher fish will be substituted. Although there are other fish which look very similar to salmon (some types of trout, etc.) they are all kosher. Further, OU policy asserts that the red colour is considered an acceptable identifying mark for kosher. 

Furthermore, the Halachic principle, "Tradesmen will not jeopardize their livelihood  -  Uman Lo Mara Umnaso" - see Shach YD [98:2]; Rav Aharon Kotler, quoted by Rabbi Yirmiyahu Kaganoff; Shu”t Chelkas Yaakov 3:10] determines that the common interests of the processing plants, the retail and food service industries, and the fishing companies, all confirm that simply for the sake of financial success and avoiding crippling government penalties and maintaining consumer loyalty, there is every reason to ensure that the package contains precisely what it claims. This is adequate to Halachically verify that a tin of tune contains only tuna.

Bishul Yisroel, ShA YD [113]
Our Sages decreed that various foods must have Kosher participation in their cooking. Tinned tuna and salmon is gutted and then steamed in order to facilitate the removal of the skin and bone. Rabbi Schachter writes in “Is Canned Tuna Kosher?” p20, that Mashgichim have reported that tuna is already edible at this point. (This is puzzling since tuna is edible and mostly deemed to be superior when not cooked, and foods that are eaten raw are not subject to the restrictions of Bishul Akkum) Accordingly, tinned tuna ought to be prohibited since it is Bishul Akkum unless there is Kosher participation at this point.

Others argue that tinned tuna is not subject to the restrictions of Bishul Akkum since such tuna is not served at a sophisticated banquet and only foods “fit for a king’s table” [a vague definition subject to significant debate] must be cooked by a Jew. While tuna can be prepared so as to be fit for “a king’s table”, tinned tuna does not qualify. OU considers whole baked baby potatoes as being fit for the King’s table, but not potato chips, wedges and crisps. Similarly canned tuna is not served at a royal table although whole or cutlets tuna are.

Furthermore, Bishul Akkum applies to foods that are cooked, roasted fried and baked but not to foods that are pickled, salted, smoked or, according to many, steamed. Other Poskim do not rely on the exclusion of steaming unless it performed in an industrial setting. The mitigating consideration being that there is no risk of social intercourse between the non-Jewish processor and the consumers.