When Harry and Tom are in Sandrine's pool room, Tom challenges Harry to a game of pool. The camera shows Tom starting to rack the pool balls, then pans up. His hand movements from start to finish only account for him placing 5 or 6 balls in the rack. He then removes the racking triangle and moves to the opposite end to break. The next camera cut shows all 15 balls are in place for the break.
At the end of the second part of the pilot, Janeway promoted Tom Paris to the rank of lieutenant. At the beginning of this episode, however, he refers to himself as an ensign, after Harry Kim tells him he should've asked Janeway to join them in the mess hall.
Power reserves on the ship are so low that Captain Janeway would need to use ration points to replicate a cup of coffee. Tom Paris however has an entire holodeck simulation running for a long length of time.