Black Tiger Steals Heart - S1-E10
Continuity mistake: Once Bakuto starts explaining to Harold Meachum how he's more easygoing than Madame Gao, the chicken on Harold's plate changes position between shots.
The Blessing of Many Fractures - S1-E8
Continuity mistake: During the fight with Zhou Cheng, Cheng does a forward flip and kicks Danny, making him stumble backwards. In the shot of Cheng lying on the ground, Danny is holding his stomach. In the shot immediately afterwards, he's holding his chest.
Lead Horse Back to Stable - S1-E11
Revealing mistake: When Danny and Colleen are fighting in the rain at the end of the episode and Danny starts explaining how they should stop fighting, raindrops from the camera can be seen dripping from the top left of the screen.
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.
Dragon Plays with Fire - S1-E13
Continuity mistake: Danny grabs the keycard off the guard with his left hand. He still has it in his left hand outside the elevator door and when going inside. But it's in his right hand when he puts his hands on the back elevator wall.
Continuity mistake: When Davos has one of the guys pinned down on the ground with him, you see the knife next to him, above his shoulder, mostly on the grey tiles. But in the next shot when he reaches for it, the knife is in a different position. It's next to him (so Davos only has to reach his hand over to the side and not above) and resting halfway on the grey and yellow tiles.
Lead Horse Back to Stable - S1-E11
Continuity mistake: When Davos is talking to Claire in the kitchen, his hands are behind his back. But in the shot before they go sit down, his hands are to his side.
Lead Horse Back to Stable - S1-E11
Continuity mistake: When Davos rolls Danny over, Danny's right hand is on the ground. In the next shot, it's resting on his stomach, but is then back on the ground before he summons the iron fist.
Shadow Hawk Takes Flight - S1-E2
Continuity mistake: When Joy and Ward are talking in the office, she's gripping the mug on the side. In the next shot after Ward sits next to her, she's now holding the mug by the handle. It switches back to the side and then to the handle again.
The Blessing of Many Fractures - S1-E8
Continuity mistake: When Danny offers Zhou Cheng money, the position of the money in Danny's hand changes between shots.
The Blessing of Many Fractures - S1-E8
Continuity mistake: During Colleen's sword fight, the position of her sword's sheath and her assailant's on the ground changes between shots.
Under Leaf Pluck Lotus - S1-E5
Continuity mistake: The heroin packet that Danny places on Ward's desk moves slightly between shots.
Under Leaf Pluck Lotus - S1-E5
Continuity mistake: After Danny speaks with Megan, he places a paper flower on her desk. In the close-up shots, the paper flower is facing her. But in the quick shot of Danny leaving for the elevator, its facing to her left.
The Blessing of Many Fractures - S1-E8
Visible crew/equipment: During the fight with Zhou Cheng, Danny's face is blurred during a shot, revealing it was a stunt double. (00:45:40)
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.