Encounter at Farpoint (2) - S1-E2
Continuity mistake: The "loose rock" Wesley falls from didn't move at all the way it did with Riker.
Continuity mistake: In the Shuttle, Q's hair is arranged in bangs on his forehead. A split second later in Ten Forward, his hair is up and back from his forehead in the familiar style.
Suggested correction: Q's powers has shown in the past that he can change his looks in an instance, as well as his location and anyone else he chooses. This is precisely what happens here.
Continuity mistake: As Data, Geordi, and Will pause to consider a route around Engineering section, the smoky mist is chest high. After the angle change it's thinner and shin height.
Continuity mistake: On the freighter, when Geordi looks at Data, the image on the Bridge view screen has Data's hair in an unkempt, or unusual style. When the scene shifts back to the freighter, Data's hair is straight back.
Nth Degree - S4-E19
Continuity mistake: When Barclay enters the Holodeck to create an interface, he calls for a chair, an input for the left and a display for the right. When Picard comes to question him, the input and display units are gone.
Continuity mistake: When checking Ian's pulse, Pulaski reaches out with her left hand, but her right arm retracts after the angle change.
Continuity mistake: When Picard, Ro and the others arrive at the refugee camp to meet with Keeve Falor, the type of uniform top Ro is wearing has its zipper at the back in the center - with no seam whatsoever at the front. When she kneels down in front of The Child, it has changed to the open-front jacket type, so Ro can touchingly give it to The Child.
Power Play - S5-E15
Continuity mistake: On the planet's surface, when the away team are knocked unconscious their positions on the ground differ significantly between shots.
Where Silence Has Lease - S2-E2
Continuity mistake: When Riker and Worf are beamed off the Yomato, Riker is on the left of Worf. When they materialize, Riker is on Worf's right.