After Sarek and his entourage enter the concert hall, the sliding doors fail to close all the way behind him, leaving a gap of about an inch or so for light to spill through. After the shot changes, the doors are fully closed, and remain that way for the rest of the scene.
In the opening scene, Jean-Luc Picard mentions to Riker that he met Sarek several years earlier "at his son's wedding". We never saw Spock as being married in any previous movie or show, but they all took place before Picard was born. Spock took a wife much later than the time of his screen appearances.
The crew are entertained by a recital that starts with a Wolfgang Amadeus Mozart string quartet, as promised. This needs four players: two violins, viola and cello. The piece that causes Sarek's tear is in fact Johannes Brahms' Sextet #1 - which would require six players, i.e. an additional viola and cello.
At the beginning of the episode as Picard and Riker are turning the corner to enter the transporter room, Picard speaks "the benefits of relations with the Legarans are incalculable", but his mouth is closed during the word "are".
In one line, Perrin flubs the pronunciation of Bendii when she says, "He [Sarek] does not have Bandee Syndrome, and that shall be the end of it."
After Commander Riker walks in on Geordi and Wesley fighting in the Legaran conference room, Wesley asks "May I be excused, Commander?", and immediately walks out of the room without any acknowledgment of approval from either Riker or Geordi to be excused.
Spiner makes no attempt whatsoever to look like he's actually playing the violin, especially with his fretting hand.
When Perrin comes to ask Picard to help Sarek complete the mission, Picard calls her "Perrian."