The Fearsome Dr. Crane - S1-E14
Continuity mistake: When Nygma examines the corpse, he pushes his right hand deep into the body. When he is caught, he holds both hands up in the air. The glove on his right hand is completely clean, when it should be covered in blood and gore.
Audio problem: When Gordon and Bullock attempt to arrest Falcone, Bullock forces two henchmen into the room and a sound of a shotgun being cocked is heard as he enters the room behind them, but he is carrying a rifle. (00:33:05)
Other mistake: While Gordon is a security guard, he has sergeant stripes on his sleeves but corporal stripes on his collar of his uniform.
Continuity mistake: At the end of the episode Fish is standing at a puddle, with three long puddles striped in front of her. After Falcon sits down with her, the camera pans back again showing where she was standing. All 4 puddles have suddenly evaporated and the additional puddles further ahead are almost gone. (00:41:05 - 00:42:10)
Continuity mistake: When Bruce follows Cat to the roof top he jumps after her. He runs and steps onto the ledge with his left foot. When the camera angle switches it shows Bruce jumping off his right foot instead. (00:18:10)
All Happy Families Are Alike - S1-E22
Continuity mistake: When Moroni arrives to kill Falconi, the number of turns of rope around the hook holding Falconi changes. First it is just one loop from the front, then the shot changes to the back and it is two. The shot changes to the front again and now there are three loops of rope around the hook.
All Happy Families Are Alike - S1-E22
Revealing mistake: When Falcone is attacked with a bazooka, notice how none of the chickens in the cages move a single muscle with the explosion right next to them.
Continuity mistake: When Dr. Thompkins is first introduced to Bullock, he reaches backward over his head to shake her hand. The shot changes and he is suddenly reaching around his body instead.
Revealing mistake: The chest of the "dead" girl on the autopsy table moves due to her breathing, and her eyelids move twice. (00:15:20)
Answer: Tabitha got her hand sewn back on, Butch didn't.