When the first set of thugs kick open the door to Jack's apartment, they shatter the inner door jam. Immediately after that, and throughout the rest of the story, the door is undamaged,
Right before the fight in the diner, Cara pours coffee over Jack's hand which is covering the opening of his mug because he does not want coffee. His right hand is resting under the table. The camera cuts to a different angle, and we see Jack take his *right* hand from the general location of the mug's top, then he shakes it as if trying to rid it of spilled coffee.
At 54:54 into the movie, Jack is asking for Alex through the door. Gary wants him to wait outside and slides back the door hatch completely, but in the next shot the hatch is slightly open, so Jack can slide his arm in and unlock the door.
After the bingo caller places the yellow B2 ball in the tray, the camera switches to Jack and Andrea, and then back to the bingo caller. The yellow ball is now gone.
The bullets that Jack/Cain pulls out out of his body are still in pristine shape. Any impact should have made the bullets misshapen to some degree.
Jack refers to himself as Qayin which is how the name Cain is pronounced in Genesis 4. However, when he mentions Abel at the 1h 33m mark, he mispronounces Abel in Hebrew, Chevel.
Jack recites a phrase in Vulgate Latin, "Leginum... Convictio... Scientia... Veritate," to mean basically, "Knowledge of the law, conviction of the truth." In actuality, this Latin translation is gibberish. "SCIENTIAM LEGIS CONVICTIONEM VERITATIS" would be the more appropriate way to write it (Romans didn't use punctuation or lowercase letters) and it would sound like "shy-EN-ti-em le-JI-s cum-VE-SI-tinam uer-ee-TA-tis." A character as old as Cain who lived during the time of the Romans would have spoken it fluently, and even if it was a little rusty, it wouldn't translate to gibberish.
When playing bingo with multiple cards, around 36mins in, Jack is suppose to be super focused. However the cards clearly show that he is not stamping the called numbers on all the cards. He stamped B10 on two cards while this number is still unstamped on at least two other cards. Also, some of the numbers you hear aren't stamped at all.