When the black background which displays the cities names in the show comes up, it reads Santiago. Now there are at least 3 mayor cities named Santiago: Santiago de Chile (Chile), Santiago de Compostela (Spain) and Santiago de Cuba (Cuba). The Santiago we see is supposedly in Chile, since the vehicle plates we see from the black van are from Chile. However, when they show Santiago as a vegetation covered hill side with houses that's incorrect, for Santiago is located on a plain at the center of a valley, and has only one mayor hill landmark, Cerro San Cristobal, the rest of it is crawling with buildings and commerce.
The cutting of the elevator cable shouldn't have worked as all elevators have emergency brakes (purely mechanical, with no need of electrical energy) fitted for in case the main cable is ever severed. It should have come to a halt a few floors down.
Why would Carter "wreck" Dr. Sinclair's hands if she was supposed to assemble something for them? She managed to do it, of course, but it seems like a large risk, especially since she has other body parts (legs, most prominently) to choose from.