The Federation science vessel found by the Enterprise carries the name USS Brittain on the hull (which is backed by all spoken pronunciations), but its name on all internal bridge displays and the Captain's log when it is replayed has its name spelled correctly as 'Brattain'.
When Doctor Crusher enters the room with the body bags, you get a clear view of the third body bag in the middle. The bag is clearly folded at the feet; however, after the hallucination when Crusher says "go away," you can see the bag has been flattened.
When Picard says "Come" after the second time his Ready Room door chimes, his right hand moves from his lips to a point halfway to the table and stops, with his head facing his viewscreen. When the camera changes, his hand moves from his lips all the way to the table and his head is turned towards the door.
Andrus Hagan is in a catatonic state when rescued from the Brattain. He is kept in sick bay for over 10 days but no one removes his shoes, gives him other clothing, or even puts a blanket over him.
As Data and Troi scan the list of chemicals, the list scrolls down. When Troi tells Data to go back, Data continues scrolling down. For Data to 'go back' to the place of Troi's interest, he would need to scroll the list up.
All but non-human personnel are negatively affected by alien telepathy and barely able to function, yet twice, when Security is summoned, unaffected humans arrive, fit and ready for instruction.
When Dr. Crusher reports on the autopsies, she plays a video file from the Captain's Log of the Brattain. This assumes that Picard had not already done so. Giving what had happened on the Brattain, Captain Picard would have watched those logs himself to learn what befell its crew.