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 an automatic, would already have been cocked after his shot at the prisoner.
After finding her father's secret office, Lara finds a Camcorder that has a post-it note on it saying 'Play me'. She plays the video but the Camcorder has a rechargeable battery which amazingly still has power after 11 years of non use. Likewise the Cassette Recorder which she takes out of a box and switches on and listens to the tape, again with batteries that have not lost power after 11 years.
The goof items 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.
During the final scene in the movie, Lara Croft is seen purchasing a set of handguns from a pawn brokers in London. In the United Kingdom it is illegal to sell firearms in pawnbrokers or other normal premises. All firearms sales are strictly controlled, regulated and limited to specific weapons like shotguns, hunting rifles and single shot target pistols and only to strictly licensed users who can prove a legal and justifiable purpose for owning a firearm. Therefore Lara Croft would never be able to walk into a pawnbroker or any other shop and buy an automatic or semi-automatic pistol of the kind shown in the movie.