Just before Dr. Bashir leaves the Enterprise, he and Data walk down a corridor chatting, and it is clearly seen that Dr. Bashir wears Starfleet Style black boots/shoes. Moments later, after he and Data part company, Bashir's shoes are now white.
When Worf grabs Jaglom Shrek, he swings him to his right, away from the promenade railing, but in the next cut, Shrek is over the railing.
Geordi La Forge plugs a cord into the side of Data's head before intentionally rendering Data unconscious to start his "dream." The cord is also in place when Data wakes up again. The cord disappears when he falls unconscious, but this moment is part of Data's fantasy POV, in which he would not visualize the cord.
When Worf grabs the rail at his station in frustration, it clearly wobbles.
In the first shot of Data lying on the mattress in his second 'vision' and Soong is walking toward him from the captain's chair, an obvious double can be seen in Data's uniform and makeup as Brent Spiner could not play both roles in a single shot without the use of visual effects.
During Data's "dream flight", a man in a black t-shirt is seen down a corridor as the point-of-view flies through the ceiling.