Continuity mistake: When Danny is about to dress his knife wound, he grabs the tape with both hands and there's nothing covering the wound. He tears the tape, still using both hands, but then in the next shot as he's putting the tape down, a gauze pad is now covering his wound.
Continuity mistake: When Danny and Ward meet Joy in her new place, Ward says "who was it who said I was being childish?" Danny is in the background, holding the folder cover open with his left hand. Shot cuts as he speaks, and his hand's suddenly on the pages with the folder cover hanging down loose.
Answer: In the comics Iron Fist is able to use the power on both hands. There is no reason why Danny shouldn't be able to. Presumably he chooses to only use the one fist at a time, focusing all his power into one hand rather than distributing it between 2.