Character mistake: When Steve is at the Smithsonian, he reads the biography of his friend Bucky. At the start of the description, the bio reads "Born in 1916...", but at the bottom of the description, it reads "Bucky Barnes: 1917 - 1944." (00:18:35)
Continuity mistake: When Steve leaps from the helicopter and onto the boat, he lands in the water. As soon as he gets on board the boat, he is completely dry. (00:05:00)
Continuity mistake: After Nick has escaped the "cops", he tells the car to give him the wheel. The shot then cuts to an overview shot where Nick is shown speeding through traffic. Just as the shot ends, he is shown about to drive past a bus, but by the next shot, the bus has vanished completely. (00:28:40)
Continuity mistake: When Steve goes to pull open the cabinets to reveal the secret elevator, there are cobwebs covering part of the cabinet. Next shot, the cob webs have vanished. (00:58:15)
Chosen answer: They were talking about the apartment Steve Rogers lives in. Pierce is saying Nick Fury bugged Cap's apartment, one of his own agents.
Bishop73