When Deanna Troi enters Tan Elbrun's quarters, as the door opens, you can see the focus mark on the floor as she enters in the long shot.
Before the star goes supernova, Tin Man hurls the Enterprise 3.8 billion kilometers away. Once they stop, approximately 30 seconds later, they see the star explode on the main viewing screen. From that distance it would take 3½ hours for the light of the explosion to reach them.
As a professional counselor, ethics require that Troi not discuss patients to others. Not only did she mention that Tam had been a patient, she went into specifics about his diagnosis and treatment.
Data says, "I'm puzzled." Data is supposed to be incapable of contractions.