During the first spiderling attack the collar and chain vanishes from around Carter's neck and then reappears.
During the spider attack, Tars Tarkas shoots John Carter's chains, but they are shown as chains around his wrists, and in the next shot her had a chain on his neck.
Vasquez rocks (made famous by the original Star Trek series and also later used in the movies as an area in Planet Vulcan when Spoc gets his Katra back) is used prolifically in this movie. So much so that it is shown as a background when Carter first shows up ion Barsoom. Then, after the Tarks take Carter prisoner and lead him to their home the rocks show up in the back ground during the fight. Then, later they are shown again when they are traveling to the Air Station. This is after they are shown to have traveled 'day and night' from their home to the air station. The budget must have been incredibly close to zero, but is it hard to at LEAST get a different angle of the rocks to mix it up a bit? Apparently it was, so the rocks show up often and make you feel like you have deja-vu watching the scenes. Claustrophobia also feels like it's just around the corner.
A Craftsman logo is clearly visible on one of the items of hardware inside the power station on Mars.
As Tarkas' men try to break into the air pumping station a zipper is clearly visible in the back of a warrior's costume.
When John Carter fights Tars Tarkas in the pit, he gets Tars in a headlock that snaps the right tusk on the actor's mask.
As Tars, John, and the Princess approach the pumping station, you can see the neck part of Tars' mask riding above his clothes. It can be seen multiple times as the conversation switches back and forth. But once they arrive inside the station, his "skin" is once again tucked back under his clothes.