The Royale - S2-E12
Factual error: 30 seconds in Geordi says: 'surface temperature -291 degrees Celsius'. (The scale only goes down to -273.15 which is absolute zero). (00:00:30)
Factual error: The second piece of music played at the concert is by Brahms and not Mozart.
The Best of Both Worlds (2) - S4-E1
Factual error: Shelby announces the Borg have entered Sector 001, and we get an exterior shot of the Borg ship flying past Saturn. The problem is that the Borg are approaching from the side of the planet illuminated by the sun, meaning they would actually be moving AWAY from Earth rather than toward it.
Factual error: When the starboard nacelle causes the ship to spin, the view of the stars on the main screen on the bridge should move toward the right side of the screen, rather than standing still.
Factual error: Picard reaches for the bowl of rotten fruit, winces in pain, and suddenly his fingernails have grown about an inch. This was due to the fruit bowl being inside an area where time was moving much faster. The problem is, in order for his fingernails to grow, blood would have to supply the needed nutrients to his fingers at the accelerated rate. Since his heart is in normal time, being away from the bowl of fruit, there is no way his fingernails could have grown like that - his heart is only supplying a normal-time-continuum's worth of blood.
Suggested correction: This entry conflates rapid growth with sped up time.
Factual error: With the Enterprise and the Romulan ship are stuck in a bubble in time and virtually stopped, the 2 ships would not be visible to the crew on the shuttle. The light entering the bubble would slow down, as would the light reflecting off the ships. All the shuttle crew would see is a "black hole" in space. (The disruptor beam was stopped in mid fire and sensors cannot penetrate the bubble).