However, Natasha's reference to working for the KGB is anachronistic; the KGB was dissolved in late 1991, when Natasha would have been about seven years old. Either the KGB (and possibly the Soviet Union itself?) still exists in the Marvel Cinematic Universe of 2014, or Natasha actually worked for the FSB, the KGB's post-Soviet successor. (Which, admittedly, the FSB is made up largely of the same people operating in the same buildings, doing lots of the same things -- they might as well be the same organization, name and government notwithstanding.)
I wonder if Romanoff isn't as young as people think she is. Hard to say for sure, but it seems weird to have Black Widow completely removed from the Cold War.
Roosevelt Island seems about right. At first, I assumed it was somewhere in Virginia, maybe around Rosslyn or Arlington. But then I realized that it can't be Arlington -- the shots of the Lincoln Memorial and Reflecting Pool from the Triskelion's POV place them slightly southward. So between that and the fact that we don't actually see Roosevelt Island anywhere in the establishing shots, Roosevelt Island does seem to be the home of the Triskelion.
Yeah, after looking carefully at that shot, it clearly is Roosevelt Island. It means that it is in DC, I thought it would have to have been in Arlington. Interestingly (or randomly), that means it's the first building in DC to exceed the height restrictions imposed elsewhere. It also means that Rt. 50 goes straight through Triskelion - that's got to be a traffic nightmare

Next question:
This has been bugging me since The Avengers: Who, exactly, does SHIELD work for? They seem to be a U.S. organization, between being staffed by Americans and the use of the word "homeland" in their name. Yet we see them answering to this "World Security Council" in both The Avengers and The Winter Soldier. Alexander Pierce is addressed as "Mister Secretary" and seems to be in charge of them, too; is he the United States Secretary of Defense?
SHIELD appears to be an international agency. It seems more akin to NATO in that it's western-based and was founded by an American man and a British woman, but it seems broader and works closely with many nations. The fact that it is governed by the World Security Council, which includes representatives from India, show it isn't exclusively American. In Avengers, the US military was actually going to help the movie with production until they found out about the Council and decided that they didn't want to support an organization that suborns American interests to an international body, even in a fictional universe.
In Agents of SHIELD, I think it's clearer. They have bases all over the world. They've got at least two non-Americans on the team. They asserted jurisdiction in Italy and South America. At the same time, not every country is a member. It seems Russia is not, based on the fact that the team had to sneak into South Ossetia from Georgia. Also, Malta certainly is not. I suspect there are little countries all over the world who piggyback off of both the security SHIELD provides and the ability to not be a member and charge a premium to shelter rich people. Finally, I get the impression from this movie that Pakistan is not, although that was more ambiguous.
ETA: Here is the quote from Seeds (courtesy spoiler tags for those who don't want to be spoiled on an episode that aired three months ago):
Quinn asks, “Who is this?”
Coulson says, “Agent Phil Coulson with S.H.I.E.L.D. We’ve never actually met, but I’m familiar with your work. All of it.”
Quinn says, “So this is a getting to know you call?”
Coulson says, “No, just a message,that the first time your aircraft drifts over any country allied with S.H.I.E.L.D., we will shoot you out of the sky.”
Quinn says, “So this is a courtesy call. Well, thank you, Agent Coulson. And I have a message for you. The clairvoyant told me to say hello.”