Continuity mistake: In one scene when Jerry is entering the Federal Building, he starts through the metal detector, and he is stopped by a guard, and is asked for his keys, so he does not set off the alarm. Problem is, the guard, immediately hands the keys back to him, through the arch of the metal detector, yet it does not set off the alarm.
Continuity mistake: When Jerry first returns to his home he unlocks the fridge and takes out a container of food. Shortly afterwards he spoons some food into his mouth. He then puts the spoon back in his mouth with the bowl of the spoon inverted to lick it again. The camera immediately cuts to a different angle. He removes the spoon from his mouth but now the bowl of the spoon is the right way up.
Plot hole: The scene takes place in Julia Roberts' father's stable. Mel Gibson explains to Julia Roberts that he was supposed to kill her father, a judge, because he was going to reopen a certain case. Gibson says that he couldn't kill him and they became friends. He further explains that he was the one to talk her father into reopening the case in the first place. The problem is, they didn't meet until after he decided to reopen it, since that was why Gibson was supposed to kill him in the first place.