When they work through the rubble at the imploded hatch, the red exercise bike can be seen in it. Yet in Flashes Before Your Eyes (2007), when Desmond wakes up naked in the jungle, he comes across the bike a distance away from the hatch.
There is no razor in the first aid kit as no sharp objects are allowed, yet a woman is seen knitting - knitting needles are not allowed on planes as they can be used as weapons.
Charlie's hair was longer in the airplane before falling in season 1. However, Jack didn't have a cut on his neck and Desmond wasn't in the plane back in S1, so hair length could be just one of those many differences.
Sayid's customs and declaration form has the logo of the United States Customs Service, which ceased to exist in March 2003. It was replaced by the U.S. Customs and Border Protection, which uses the logo of its parent agency, the Department of Homeland Security. Updated forms would have been used by September 2004. However, considering there were changes in the characters' lives, it's safe to assume there were also changes in government agencies in this alternate universe.
After the hydrogen bomb exploded, the crew apparently returned thirty years back into the future - present time - yet, the DHARMA van in which they transported Sayid in the jungle still appears to be brand new and running very well as it did back in the 1970s.
However, considering the characters didn't age, and back in S5 raft and canoes also moved forth and back with the characters, one could argue the van did travel along with the characters.
When Sayid looks at Nadia's picture for the first time the passport is Iranian and not Iraqi. The second time the passport's color is green, but Iranian passports are dark red.
Oceanic flight 815 is shown from the front landing as a Boeing 777 with 12 wheels under the wings. When shown from underneath, there are only 8 wheels.