Goofs

It is said that Wesley is a 4th year cadet. However, he started at the academy in 2367, had to retake a year in The First Duty (1992). This would make Wesley at most a 3rd year cadet. This is further solidified by the fact Wesley wears only 3 cadet pips on his collar, not 4.

Beverly speaks to Wesley about the Traveler, but mistakenly says that he is from Tau Ceti. Both Where No One Has Gone Before (1987), and Remember Me (1990) had established that the Traveler was from Tau Alpha C. However, this may have been retconned because 'Tau Ceti' is correct astronomical terminology (Star 'T' in the constellation Cetus) but 'Tau Alpha' is meaningless. (Stars are designated by a Greek letter and the name of the constellation, e.g., Alpha Geminorum, star 'A' in Gemini.)

When the Traveler first appears in Where No One Has Gone Before (1987), he says to Capt. Picard in private that Wesley is special, like Wolfgang Amadeus Mozart is to music and asks him to keep it to himself, especially don't tell his mother. Picard agreed and was never shown telling Beverly that secret. Here, Beverly relays to Wesley the same statement, about him being special like Mozart. How did Beverly find out what the Traveler told Picard? However, it is common (possibly even a cliché) to use Mozart as an exemplar when referring to child prodigies.

The admiral didn't have any of her canapés.

Sound crew visible on the right side of the frame at 19:40. The camera crew corrects by increasing zoom.

In the opening sequence, Picard refers to Admiral Nechayev as "Fleet Admiral." However, her insignia only has 3 pips encased in the square, which is the rank of Vice Admiral.