After Vogel killed one of the prisoners in the camp with his gun, he points it towards Lara. He then cocks the gun. This is purely for dramatic reason as the gun, being a semi-automatic, would already have been cocked after his shot at the prisoner.
At around 57 minutes, after Lara escapes Mathias (as the scene turns to night), there is a close up of a Bearded Dragon in a tree. This is a desert lizard native to Australia and could not survive the humidity of the island.
When falling in the river Lara ends up on a rusty crashed airplane.
The body work of that plane would had been made of aluminum, as iron is way too heavy. This would not result in a brown rust patine, as aluminum turns white when it corrodes.
The goof item below may give away important plot points.
Lara takes many unnecessary risks in the final battle with Vogel. She approaches him from behind, and could easily have kicked him down the shaft that the makeshift bridge goes across. Instead, she jumps out onto the bridge, dangling off the side as the nearly falls into the pit, putting herself in a vulnerable position. She then takes the diseased finger and crams it down his throat, potentially risking getting herself infected. And on top of this, she kicks him after he's clearly infected, running the risks of infection herself once again. All of these risks could have been avoided if she'd simply surprise attacked Vogel and knocked him down the chasm.