(At around 2:00) When Guinan is talking to Dixon Hill's secretary, Guinan's cigarette looks longer and has less ash in the camera shot from her left than the previous shot from her right.
Picard tells Data that he would would "likely be stripped down" to his wires to find out what had gone wrong. Since Data's legal rights as a sentient being had been established (in "The Measure of a Man"), this would not have happened.
When Guinan shows her garters to Dixon Hill's secretary, the close-up of her legs may appear to be those of a white woman, but are actually Whoopi Goldberg's legs. The lighting of the scene makes the skin appear lighter than it really is.
Data, being an android, would not have had the emotions for him to have that little smirk at the end when he realized the crew, and Capt. Picard, were fooled by his fake explanation of the incident. However, Data often imitates human behavior, and probably did so again.
On the holodeck, in Dixon Hill's office, Johnny is lying dead on the ground, facing the floor. You can clearly see the actor moving his eyes as Picard moves his head to face the ceiling.
Despite gunfire shattering the window in Dixon Hill's office and killing a character, the secretary Madeline does not investigate and moments later she takes a phone call like nothing has happened.
While looking over Data's shoulder at Picard, we see moving shadows on Data's back. They are in a room with no moving equipment, and no one else is in the room.
After the surprise travel through the wormhole, Riker says the Enterprise is a day's travel from where they had been. A sensor probe is launched to the planet the Enterprise had been about to study and, somehow, in a short time (not even an hour's travel, as implied), the probe makes it not only into sensor range but into visual range.