Episode #1.4 - S1-E4
Continuity mistake: Thomas and Grace are sharing a drink to celebrate her employment with the Shelbys. Thomas pulls out a cigarette, puts it in his mouth (correctly), and then turns to the camera to reveal a backwards cigarette. (00:43:00)
Episode #1.5 - S1-E5
Continuity mistake: When Tommy enters the office where Grace is working on the books he steps forward, leaving the door open, to draw a black star on her ledger. When he turns to leave the door is shut. (00:03:40)