In his flashback, Charlie runs from the flight attendants to the front of the plane and locks himself in a bathroom. During the turbulence, he leaves the bathroom and straps himself in a business class seat. We later learn that the front section of the aircraft (business class) separated and landed somewhere in the jungle, yet Charlie is a fuselage-section survivor on the beach.
In the opening sequence, after Jack removes his bloody undershirt, Kate sews up a large wound in his back. Yet, later, in the cockpit scenes, not only is Jack's rainplastered, semi-transparent undershirt pristine white, it (and his back) is perfectly smooth - no bandages, no stitches.
During the flashback sequences for both the pilot and the finale, different characters are meant to be traveling through different sections of the plane, although it appears that, with the exception of business class, the same section was used for filming but with different people. This becomes a problem when spoken lines referring to seat numbers as well as the footage from right before the crash doesn't match at all to the boarding footage in the finale.
The Oceanic airplane is supposed to be a Boeing 777, but when you see Jack running through the wreckage you can see that the main landing gear of the plane has only 4 wheels instead of the six a B-777 would have. Also, when Kate, Jack and Charlie reach the front section of the plane, in several shots where you can see the instruments of the cockpit, there are 3 engine indicators instead of the two a 777 would have
When the scene where the engine explodes is slowed down a black object can be seen flying down and hitting the engine. While some fans believed that this may have been the Monster destroying the engine, the producers confirmed that it is merely a CGI rendering error and that what was meant to be debris flying away from the exploding engine instead became an object hitting it.