Continuity mistake: After the Stormtrooper tells Darth Vader the Death Star plans are not in the main computer, when Vader lifts the Rebel off his feet by his throat as the Rebel tells him they intercepted no transmissions, take note of the leg plates on the Stormtrooper to Vader's right. In the wide shot, the Stormtrooper's left leg armor does not have the knee protector plate (it looks as if it's at his right knee because the extra switched them), but in the next closeup the knee plate appears at his left knee, as it should be. The trooper also appears to go from right handed to left handed weapon carry. (00:05:40)
Revealing mistake: While Poe leads the aerial assault on the oscillator, in the closeups of Poe and other X-wing fighter pilots, note the cockpit windows at the pilots' left and right have identical marks and scratches in their individual X-wings. It's particularly noticeable when one closeup follows another.
Continuity mistake: When Vader's shuttle is approaching the Death Star, the crew in the control room of the Death Star are wearing black gloves. One of them then reaches forward to press a button, but in the close-up of his hand pressing the button, the hand is not wearing gloves at all. This can only be seen in the widescreen version. (00:02:25)
Continuity mistake: When one of the stormtroopers unties Han Solo before he is put into the carbonite, watch his wardrobe - he has a disappearing / reappearing jacket on. This is fixed to an extent on the DVD - the jacket is now lightened to almost match his shirt, but it's still shiny like leather. (01:32:05)
Continuity mistake: When Anakin attaches 3PO's right eye, one shot has the eye in his left hand, then the angle changes and the eye is being applied with the right hand. (00:37:20)
Continuity mistake: When Anakin is in the medical centre lying on his back being transformed into Darth Vader, you can see the main part of the mask being lowered into place but Anakin is not wearing the neck section of the mask that it connects to. We then see the main part lowering directly downwards, in the next shot the neck section is in place. (02:01:20)
Continuity mistake: During the sequence where Obi-wan goes to meet Yoda regarding the absence of Kamino from the Jedi Archives, look closely at the collection of children Yoda is training. While most are human, there is one that is alien, with a reptilian face of dark skin. He sure moves fast, because at first he is at the back in the centre of the group of trainees, in the next shot he is at the front of the group of trainees, and by the end of the scene, he is on the far left, yet we never see him, or any of the other children, move. (00:36:25)