Towards the end of the film, Sharon Gale, David's wife, receives the silver suitcase with the post card from Berlin in it. The postcard was mailed from San Francisco to Texas but has no postmark on it in the upper right hand corner as it should.
Near the end of the film, when the protesters are outside David Gale's execution, there is a clear shot of a large banner hung across a barricade which reads "Mark 6:10 Murder does not stop Murder." Mark 6:10 actually reads "And He said to them, Wherever you enter a house, stay there until you leave town." (NASB), so the bible quote actually has nothing to do with murder at all.
When Bitsey found the tape in Dusty's house and put it on the VCR we see "Constance" hand-written on the sticker. When she eject the tape from the VCR the sticker had changed it's then machine written or printed.
When Zack and Bitsey are re-creating Constance's death, you can clearly see Zack bump the tripod-mounted camera as he moves. But in the next shot, the view on the monitor is the same. Such a jolt would have severely changed the composition of the shot.
When Bitsey Bloom was watching the tape in the motel room before she asks Zack to go re-create the crime scene. A quick short close up of Zack sleeping showed him wearing a watch. Before and after this close up he was not wearing one.
At the end when Kate Winslet receives the Fed Ex box she opens it easily from the end. Fed Ex boxes have pull tabs that you pull to open, and if you decide you want to open the box at the end it is not as easy as she made it look.
Huntsville Texas is about four hours away from Austin Texas, yet Bitsy drives back and forth between the two several times during the film and is able to make her 3:00pm meeting time with David in the prison.