Right before beaming down to Atrea IV with Data the second time, Dr. Tainer is wearing heels. When the transport is complete on the surface, she is wearing low-heeled boots.
When Data, Juliana and Pran are talking in the caves, the perspiration on Juliana's face diminishes and increases from shot to shot.
(at around 30 mins) Data and Dr. Juliana are jumping off the cliff, down to the pattern enhancers. The rock that Data lands on bounces back slightly, as though its actually a trampoline of some kind.
When Dr. Tainer leaves Data at Deanna's door, the door opens automatically without Data pressing a button or otherwise announcing himself.
When Data, Geordi and Juliana are making calculations in Engineering, the picture goes through a slight blurring effect, which could mean a fault in the camera lens.
At around 9 mins, whilst Lt. Cmdr Data is searching the Commercial Transport Database Archive, the passenger destination listed for Noonien Soong and Juliana O'Donnell is MALAYA IV but the planet is actually referred to (in speech and subtitles) as MAVALA IV.
When Data enters sickbay, he is carrying his violin and bow, as if he had walked to sickbay directly from the recital in Ten Forward, yet, when he is told to report to the transporter room because of an emergency on the planet, Dr. Pran Tainer has just been injured on the planet's surface. The time line makes no sense; both Dr. Pran Tainer and his wife, Dr. Juliana Tainer, have been present at Data's recital. How could the male Dr. Tainer have had time to transport to the planet's surface and begin work? And why isn't the female Dr. Tainer still wearing the outfit she had worn at the recital?
When the hologram of Noonien Soong talks to Data on the holodeck, he talks of Juliana leaving him, yet there is no way that he could have included this information in her memory chip, as she would have left him.
Data says, "Yes, sir. We'll be returning to the beam-out point shortly." It was established early on (though he did use contractions in the first several episodes, before show runners had decided he couldn't) that Data doesn't commonly use contractions.