When Beverly is examining the room full of dead bodies that suddenly are all sitting up, she closes her eyes and says, "Go away." She then opens her eyes and all of the bodies are laying back down. If you look over her right shoulder when she first opens her eyes, that body is still in the upright position. It is not, however, when the camera angle changes.
Picard refers to the science vessel as the USS Brattain and that is how it is referred to on on-screen diagrams etc. But the exterior shot of the ship's main hull shows the name USS Brittain.
When Data talks to Troi about one electron circling one proton in a hydrogen atom, the picture they are talking about actually shows an atom of deuterium with one electron circling one proton and one neutron, and the text on the screen says "Hydrogen stored in the form of deuterium".
Aliens: (repeated) See the eyes in the dark, one moon circling.
Data: Sir. As my final duty as acting Captain, I order you to bed. I shall do the same for all personnel.
Picard: Certainly, Commander Data. And...thank you.
Data: Pleasant dreams, sir.
Ensign Peebles: Someone's still here!
Geordi: What did you say, Ensign?
Ensign Peebles: Can't you hear it? There's someone still alive on the ship! I heard...I mean, I thought I heard...
Geordi: The ship was searched thoroughly, there's no one here.
Ensign Peebles: Sorry sir, my mistake.
Geordi: Don't worry about it. There were 34 people found dead on this ship. That's enough to make anybody uneasy.
Gillespie: Kenicke in Engineering told me he saw a man in an old Starfleet uniform riding the lift near the engine core. But when the lift got to the top, there was no one on it.
O'Brien: Ghost stories?
Gillespie: There's more. There's lots more. There are strange things happening on this ship, O'Brien.
O'Brien: I'm surprised at you, Gillespie. A Starfleet officer? I have better things to worry about than shades and spirits.
(Guinan fires phaser rifle in 10-Forward)
Ensign Gillespie: What is that?
Guinan: This is a little souvenir I picked up from Magus 3. That was setting number 1. Anyone want to see setting number 2?
A ton of inside jokes can be heard in this episode. Neussite 283 (Wendy Neuss), Mooride Polyronite 4 (Ron Moore), Bio-Genovesium (Cosmo Genovese), Takemurium Lite (David Takemura), and Hulzelite (Gary Hutzel) were named for various behind-the-scenes people.