Visible crew/equipment: When the Blockade Runner is being attacked, just before C-3PO says something like: 'Do you hear that?' to R2-D2, he turns his head and the camera crew is visible on his temple.

Continuity mistake: When R2D2 is captured by the Jawas, a Jawa welds a restraining bolt to the middle of a panel on R2. When the shot changes to a close up, it's being attached to the top of the panel. The shot changes again, and it's welded to the middle again.
Continuity mistake: In the garbage crushing facility, when the walls are coming in, you see them with about 15 feet space, then it zooms to the actors, they talk for about 5 seconds, and then it zooms out again with still 15 feet of space. The walls are coming in for about a minute. At the rate they were moving, they should have been crushed in around 20 seconds.

Other mistake: When Han Solo, Luke, Obi Wan, C3PO and R2-D2 are on their way to the Millennium Falcon for the first time there is a scene where they have to walk down a few stairs. If you look carefully you can see that R2-D2 is struggling to get down the stairs but in the next shot he's down with the others.
Continuity mistake: Just after the creature lets Luke go, Leia says, "It could be worse." In the next shot (after the compactor makes its first sound), Luke can clearly be seen saying, "What's that?", but his question has been edited out.
Revealing mistake: When the Millennium Falcon exits from hyperspace where Alderaan was, a TIE fighter follows them. There is a shot where it passes in front of the Falcon and then disappears.

Continuity mistake: When Luke and R2 are doing the trench run, a tie shoots at Luke and blows the top of R2's head off. But in the next scene R2's top is on again.
Continuity mistake: During the Death Star trench run, Wedge quits because his X-Wing is damaged. The sky behind him changes from grey to black in the same shot.

Continuity mistake: When Luke sees the holograph of Princess Leia for the first time, and says, "Who is she, she's beautiful," Mark Hamill's hair is rather tousled. In the next shot of him, it's neatly combed. Then, when he gets up and says, "Well I don't know anyone named Obi-Wan...," his hair is tousled again!
Continuity mistake: Widescreen version: In the trash compactor, Han says to Leia, "Get on top of it." In the next shot, Leia can be seen in the background, in a totally different position from the previous shot. For example, she is holding the pole differently. (01:20:25)
Continuity mistake: When in the Death Star, there is a shot of five stormtroopers standing next to the Millennium Falcon. Two of the stormtroopers are right next to the boarding ramp. The camera instantly changes to a higher point of view and the two stormtroopers have moved about four feet farther away from their original spots.

Continuity mistake: When Luke has been knocked unconscious by the Sand People and Obi-Wan appears and scares them off, there's a shot of Luke lying there and one of his sleeves is in disarray, halfway up his arm. But when Obi-Wan checks his pulse, he does it right through a fully-covered-by-the-sleeve wrist. (00:28:25)

Continuity mistake: In the scene just before Luke goes to eat dinner, C3PO has a towel or rag in his hand in some scenes, and it is missing in others. This continues as he admonishes R2 about replaying the message.
Revealing mistake: Special Edition: When Luke and Obi-Wan are arriving in Mos Eisley to find a pilot, the Ronto in the background throws the Jawa riding him to the floor. When the Jawa falls to the ground a puff of dust is seen and a thud is heard, but look closely - he never actually hits the ground.
Continuity mistake: When Luke first sees the holomessage from Leia, she is bending down to stop the recording while still saying "Help me Obi Wan Kenobi, you're my only hope." When the message is viewed for the second time, she finishes speaking, looks around, and then bends down to stop the recording.
Revealing mistake: Original version: When the Gold Leader says to the Red Leader "Red Leader, this is Gold Leader" at the start of the Battle of Yavin, the two Y-Wing fighters outside his cockpit suddenly disappear. (01:46:05)
Continuity mistake: After the Stormtroopers have captured Leia aboard the Blockade Runner and are leading her to Vader, one Stormtrooper's armour is visibly damaged (http://s253.photobucket.com/albums/hh67/RoofingGuy/BrokenStormy.jpg). For the close-up of Leia, the damage has been masked with white gaffer tape (http://s253.photobucket.com/albums/hh67/RoofingGuy/FixedStormy.jpg). [Timecode from 2008 Widescreen DVD release. similar time on the "Theatrical Release" bonus disc.]. (00:07:25)
Continuity mistake: During the fight against the TIE fighters, the interior shot shows the turrets on the Falcon both point straight up and down respectfully, when in other shots the top turret for example is facing forward.
Suggested correction: There is no objective up or down on a spaceship. The artificial gravity for the turrets are at 90 degree angle to the rest of the ship.
You missed the point of the mistake. Luke and Han are sitting so their backs are parallel to the deck of the Falcon, the guns are then perpendicular to their back, making them perpendicular to the deck of the Falcon. But in exterior shots, the guns are more parallel to the deck than they should be.
Continuity mistake: When we see Ben, Luke, R2-D2 and C-3PO on the cliff looking at Mos Eisley Spaceport, you can see Luke's speeder behind the two droids, but when we see a close-up of the four characters, the speeder is nowhere to be seen. (00:42:30)

Continuity mistake: In the DVD version, after Alderaan is destroyed we see Luke practicing with his lightsaber and the color is green. When he resumes practicing later on, the color is blue.