Continuity mistake: Toward the end John Murphy gets a collar around his neck. In subsequent shots the lock on the collar is alternately locked / open. (00:34:00 - 00:35:00)
Continuity mistake: When going to retrieve Murphy from the dropship, after Bellamy subdues his sister, his gag is covering his mouth. Then, as Pike moves towards him, suddenly it's magically not. (00:22:20)
