Plot hole: There's no way Dr. Lynn Waldheim's coat would have fitted Carter.
Other mistake: When Carter/Cain is putting the body in the Taurus (Jack's car), we see a clear shot of the licence plate '2ABI111', then we see the same plate on the Volvo he pushes into the lake. And it's not as if he switched plates because later, the same plate is still on the Taurus.
Continuity mistake: When Carter goes into his daughter's room after he sees his wife on the monitor, the lights are off. In the first shot of the light switch, it's down, in the off position. In the next shot, it's in the up position, with the lights still off. In the third shot, it's back down.