(At 10 min 45 s) When Raffi gets up from the table, she takes the red wine glass and bottle with her. Moments later, the glass is still visible on the table.
When Picard meets Captain Rios for the first time, he is seen standing behind him and folds his arms. After cutting to a shot of a drink being poured, Picard's arms are shown to be unfolded and he holds them again once more.
After Rios argues with the ENH on board La Sirena (in orbit), a falling star is seen out the window, against a background of stars. Falling stars are actually meteors, which only light up while they are passing through the atmosphere, which means the meteor must be between Earth and La Sirena. The background directly behind the meteor should be Earth itself, not stars. The only way to see a meteor against a background of stars is if the observer is inside the atmosphere, looking up at the meteor.
Rios is introduced smoking a cigar. An important bit of Star Trek lore is that tobacco smoking has been completely eradicated in the Federation. However, it would also be consistent with Trek lore if this were a specialized holographic cigar that gives the user all the pleasure and none of the health hazards of a real one.
It is stated that Picard is paying Rios for his services, and that said services are "expensive," but it is not mentioned how or why. Previous Star Trek material (including a memorable speech from Picard in Star Trek: First Contact (1996)) established that the Federation does not use money. However, Picard did not say how he was paying. Even in a money-free society, people are presumably remunerated in some way for their services. A whole society or federation of different societies, no matter how enlightened, cannot survive on the altruism of volunteers.
The preface begins in the year 2385, with mention of the Romulan supernova. However, it was mentioned in Star Trek (2009) that the supernova took place after 2387.