When Edgar Burroughs is given his uncle's private journal, he first turns the book so that he can open the lock with his right hand. After the attorney leaves, he turns it another time, just to put it in the same position again.
After John Carter has saved Dejah Thoris from the collapsing airship, the Tharks hand him their wager.
He then takes off the necklaces and other jewelry except for a flat white neck ring.
The camera switches to Dejah and back to Carter and the neck ring is gone.
Martian gravity is 2.7 times weaker than Earth's, which means that a human on Mars would be able to jump 2-3 times higher or farther than on Earth. Carter, on the other hand, is able to make jumps some hundred times greater even with another person on his shoulders.
Carter's Confederate record states that he was "decorated six times, including the Southern Cross of Honor." In fact, the Confederacy never issued medals and only added a few names to a "Roll of Honor." The Southern Cross of Honor was a memorial recognition created by the United Daughters of the Confederacy in the late 1890s, 30 years after the Confederacy was disbanded.
In the beginning of the film, John Carter is told that to send a telegraph he must choose a minimum of ten words. The letter is shown as only containing eight words. However, telegraphs have always had a certain number of words as a minimum cost. It cost however many cents per word, but the minimum was ten words that it would cost, not the minimum number of words that can be sent.
The Thern watching over John Carter would have no reason to believe that he actually found a medallion in the Orchades, since he knows the whereabouts of his peers, and would know that no Thern died/lost his medallion in this location.
The goof items below may give away important plot points.
When Dejah Thoris is being prepared for her wedding she is wearing a traditional Zonangan dress and red lipstick, but the lipstick color is inconsistent when she asks him to stay and fight for Helium.
When he does not answer and hides his ring hand she turns away. If you look closely you will see that her lipstick has now been expertly reapplied and is a lighter color, almost peach.
When John Carter first tries to leap over the white ape, the chain linked to his ankle drops him short about halfway across the arena. A couple of minutes later, after his chain gets tangled around the ape, wrapping around its enormous body several times, the amount of free chain looks to be nearly the entire length of the arena.