Continuity mistake: When Jack speaks to Michael and Jin, as they build the raft, and then when he walks up the beach and inquires about Sawyer's trouble with his head, the backpack that Jack carries on his back is nylon, black/green with white trim. Yet, when Sawyer asks, "Sensitivity to light, that bad?" the backpack is suddenly transformed into a solid black leather, of an entirely different style. Then, in following shots it jumps back and forth.
Continuity mistake: When the marshal and Ray drive their vehicles down the long road, the endless line of telephone poles are on their left as they drive, with barren land on their right. However, when they pass the third vehicle the poles are on their right and then repeatedly change sides in the following shots. (This has nothing to do with camera angles.)
Deliberate mistake: As Ray drives the pickup truck, an oncoming vehicle beeps and the marshal heads behind Ray's pickup. In the shot through the cab's rear window facing the bed, as the marshal pulls behind, the bed's side wall interior is seen (note the metal loop tie down on top) and the entire tailgate is gone; yet the tailgate is intact later, when the pickup flips over. The tailgate was removed for the shot to allow visibility of the marshal's vehicle.
Continuity mistake: When Kate finds the pilot's wingpin in the mud, the pilot's reflection is seen in the water as he lies on the branches above Kate. When Jack approaches they all look up and in the overhead shot the pilot's position differs and he lies on different parts of the branches, note their shape.
Continuity mistake: When Sawyer shoots "Sawyer" there is a 15 ft tall grounded lamppost at the corner of the link fence, with an overhead curved head giving off the dramatic spot of light in the wet darkness, near the trash receptacle. However, earlier when Sawyer gets out of the car at the Sweet Shrimp, as he checks his gun, that towering lamppost is non-existent.
Visible crew/equipment: While Jin is cuffed to the wreckage, Sun points to her wrist and explains in Korean, but Sayid shouts, "The cuffs stay on!" At the start of the next shot, a crewmember's arm is seen holding the reflector screen to Sawyer's left, as he makes a sarcastic comment.
Continuity mistake: After Jin is pulled off Michael, when Sawyer removes the marshal's handcuffs from his pocket there is a very short link chain dangling - about a couple of inches. However, when Jin is cuffed to the wreckage the link chain is considerably longer - about a foot.
Revealing mistake: With Marshal Mars in pursuit, as Ray drives his pickup, he holds the steering wheel with his left hand, and his stiff prosthetic right arm is down at his side. When Kate grabs for the steering wheel, in the side exterior shot the stunt driver is quite noticeable, as he grips and turns the steering wheel with his good right hand/arm.
Other mistake: The Monster appearing in the pilot and causing the turbine to explode is a mistake (not trivia). This is actually an artefact of poor CGI effects that was left in the show in error. It was confirmed by the producers. You can see it best here: http://www.lostpedia.com/wiki/Image:Turbine_Explosion.gif.
Continuity mistake: Season 3, episode 2, "The Glass Ballerina". When Jin is in the hotel and is about to kill Jae Lee, he holds a pillow to Lee's head and presses his gun against it. At first, the gun is pointing to Lee's cheekbone, but when it cuts to Lee as he is sobbing "I'm sorry. I'm sorry", the gun is much lower, and pointing to his throat. Cut back to Jin, and you can see the gun is once again pointing to Lee's face. There was no time for Jin to move it between shots, and Lee did not move nearly enough to cause this changes.
Continuity mistake: Jin is handcuffed in season 1, "House of the Rising Sun" and the cuff remains on his left wrist until season 2, "What Kate Did" when Locke removes it. The handcuffs have a distinctive shape - a single strand connected via pivot to a double strand with the lock area. When Jin is initially cuffed to the plane wreckage, the single strand faces out at his wrist, but in following shots, in this and all the subsequent episodes, the handcuff actually switches sides repeatedly, going round his wrist the opposite way.
Continuity mistake: When Charlie and Hurley are talking to Jack about the water, Jack then shouts something like, "I'm not making any decision," and in the background two people walk by - they move from right to left. After a cut to Charlie and Hurley when Hurley asks "Why?" it cuts back to Jack, and the same two people walk from right to left again.