David's papers are written in Hebrew, but have Indo-Arabic numerals which came into use towards the end of the first millennium CE. They would not be found on any document from the time of Christ or earlier.
After Jimmy (a.k.a. "The Last Martyr") dies, it can be seen through the windows on the inside of the prison that the morning daylight turned to darkness because the Sixth Seal was broken. But when they are wheeling Abby from the door to the prison to the ambulance, you can clearly see daylight when it is supposed to be dark out. Then on the inside of the ambulance, it is dark again.
When Abby visits the old rabbi's apartment, the mezuzah on his doorframe is tilted the wrong way. (It should be tilted top-inward.) Avi's (the fellow across the hall) is also placed incorrectly, as it is straight up and down, and should also be tilted inward.
Israeli Defense Force armored vehicles and trucks are not marked with a solid blue Star-of-David, as portrayed at the beginning of the movie; this shape is the emblem of the Israeli Air Force. Furthermore, IDF ambulances are marked with a red Star-of-David rather than a Red Cross, as depicted at the same scene.
When Abby visits David's room for the first time, she hears creepy audio coming from his shortwave receiver. The receiver's back panel clearly shows no antenna connection of any kind thus making any shortwave reception impossible.
At the end the earthquake starts in the execution room of the prison. It's also seen in the hospital, at least a half hour later. Earthquakes rarely last more than a minute. However, it's not clear this was a continuous quake; the hospital quake could have been an aftershock. In addition, it *is* the end of the world; the seismic phenomena could have been something previously unknown.