Factual error: The communication delay for earth-moon communications is around 2.6 seconds. Yet Emma's daughter simply dials a cell phone and is connected to her Mom in space past the moon in less than that. The communication has no time lag. (00:18:45)
Factual error: Picard tells his manservant that Laris and him are more needed at the Chateau than with him in space because there's less than a month left before the harvest. Without being privy to the knowledge of a XXIV century agronomist, grapes at the Chateau are grown with traditional methods in a climate that looks reasonably similar to our own. From the establishing shot at the beginning of this episode and what we could see by his walk in the vineyard in the previous, there are no grapes forming, ripening, not even flowers. Hardly the look of a vineyeard close to harvest. (00:07:00 - 00:36:10)
Factual error: In Massachusetts, Atticus, Leti and George are attacked by the local sheriff and his deputies, who are patrolling the county roads. In Massachusetts, sheriffs run the county jails, but they do not (and did not) handle routine policing, which is the responsibility only of municipal police departments.
Factual error: Paul tells Shea that he has a condition called Sporadic Fatal Insomnia. Later, Shea finds a fork in a bag labelled Abby. Paul explains that Abby is his daughter, and he wants to test her DNA, because she has a 50-50 chance of contracting the disease. This is false. Sporadic Fatal Insomnia is not hereditary. Fatal Familial Insomnia is genetic and is the inherited form.