Continuity mistake: In the scene right before the shuttle's crew finds the Romulan ship and the Enterprise, Geordi calls the shuttle craft's cockpit to explain the temporal disturbances. Captain Picard, Troi and Data walk into the shuttle's cockpit room and Troi puts her right arm on Geordi's chair. As Geordi, Data and Captain Picard are talking you can see Troi's wrist hanging off the chair, but when the camera cuts directly in front of Geordi her whole wrist is on the chair. The camera then cuts back and you can see that Troi's wrist is still hanging off the chair.
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.
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Plot hole: They have already shown that anything that comes into contact with the time bubbles is immediately affeceted. The engine running 47 days non-stop, the fruit againg, Picard's hand aging, etc. Geordi creates subspace isolation field that allows them to beam off the shuttle and onto the other ships to investigate. Problem is, the second the transporter beam hit the time bubble, it would have stopped and never materialized because it would have been affected by the extremely slow passage of time in that bubble. The warp core breach was affected as was the disruptor fire so the transport beam would have been easily affected. And they have never shown that have been able to alter the transporters in such a manner that would allow them to beam over.
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).
Plot hole: When Picard, Geordi, and Troi encounter one of the first time disturbances it results in one of the runabout's nacelles using up all of its fuel. Data says this is due to it having been in operation for 47 days (according to the plasma conversion sensor). After this the Captain reaches for the bowl of rotting fruit which causes him to scream in pain. The other crew members rush in and Troi scans his hand. She tells Picard that his hand is metabolizing at approximately 50 times the normal rate. Data and Geordi then discover that the temporal disturbance which covers the fruit also covers the nacelle that has lost all of its fuel. Data also notes the disturbance extends outward from the hull, about 17 meters from the ship and is spherical in shape. The problem here is that according to what Data said earlier the engine was active for 47 days even though it had only very briefly come into contact with the time distortion - maybe 1 second at most, but likely far less time than this since the ship was at warp when the fuel was consumed. So if we assume the engine was in contact with the fragment for 1 second then time is actually moving at 4,060,800 times the normal rate - not 47 or 50 times normal.
Continuity mistake: In the scene where Captain Picard reaches for the aged fruit, he screams while holding his right wrist with his left hand. As Troi, Geordi, and Data rush in you can see Captain Picard holding his wrist up in the air. The camera then cuts directly in front of Captain Picard and you can see Troi scanning his wrist but he isn't holding his wrist anymore. The camera then cuts directly in front of Troi and Geordi and you can see that Captain Picard is still holding his wrist. The camera then again cuts back to Captain Picard and he isn't holding his wrist anymore.