When Picard meets Perrin on the Enterprise, he gives her a cup of mint tea that is filled up to a marked line on the mug.
Dr. Crusher asks Data if his ears can be removed, and Data tells her they are fully integrated. However, when Data first encounters his brother Lore in Datalore (1988), Lore's ears are detached. In Brothers (1990), Dr. Noonian Soong, who created Data and Lore, says they are virtually identical except for some programming.
Crusher tells Picard that, if he wants his prosthesis to fit, he has to trust his tailor. A tailor fits and modifies clothing, not prostheses. A more appropriate term would be "prosthetist." However, Dr. Crusher is using a metaphor as a jest, not being factual.
When the Enterprise shoots the scavenger ship, they are very close to one another, yet when the ship explodes in a wide shot, the Enterprise is nowhere to be seen. The ship hadn't been ordered to move and should have been close enough to be visible in that shot. A stock footage explosion was used.
Riker orders the Enterprise to hide among the ship graveyard, keeping only life support and sensors active. When the ship approaches, the Enterprise crew scan it to determine its cargo and combat capabilities. It has been shown repeatedly that a ship being scanned can detect the scan. The Enterprise's scan of the scavengers should have alerted them to its presence.
At several points, Klingons speak in their native tongue, ostensibly so Picard and Data can't understand them. As Picard and Data wear universal translators, and all dialogue is conventionally translated for the audience's comprehension, both the Starfleet officers and the audience should have heard all of their speech in English.
Picard is sent on a dangerous mission into enemy territory. Ignoring whether it would be wise for Starfleet to send someone like Picard on such a mission, Riker has made it clear that part of his duty as first officer is to ensure the safety of the crew, including the captain, who is seen as too valuable and whose proper place in on the bridge of his ship. It has been a major plot point in numerous episodes that the captain must stay on the ship. Riker makes no protestations whatsoever about Picard leaving on the mission.
As part of his Romulan disguise, Picard was required to wear a hairpiece. However, Star Trek VI: The Undiscovered Country (1991), which this episode was created as a tie-in to, showed a Romulan with a receding hairline. Clearly Romulans also experience male pattern baldness and there would be no reason Picard would need a wig to blend in.
When Dokachin accesses the Enterprise's computer and downloads the registry of the Vulcan ship they were looking for, he says the Stardate of arrival was "41344", although the computer display clearly shows "41334".