Dr. Watson makes a comment about the stethoscope around Adam's neck. The ear pieces are hanging on Adam's left side. In the shot in the hallway, the stethoscope is now hanging with the ear pieces on his right side.
When Adam returns from obtaining blood from Dr. Watson, Eve has discovered the gun with the wooden bullet. Adam handles the doctor's bag as if it were empty rather than containing several cylinders of blood.
When the power fails in Adam's house, all lights and appliances cease functioning instantly but one can still hear the record turntable slowing to a standstill over several seconds.
The "morning" or evening, rather, after their night at the club, Eve wakes Adam and he asks, "Is it dark outside?", to which Eve replies, "Yes." However morning sunlight can be seen shining on the nightstand, through the window beside them.
There is no way to get from the USA (Detroit or Chicago) to Spain (Madrid) only flying at night. The flight will take at least 8 hours and will cross 5 time-zones into the east towards sunrise. So night would take at least 13 hours.