Other mistake: After Cage calls Gandolfini and tells him he knows about the murdered girl, Gandolfini uses the telephone. There are 13 beeps, then Cage replays it and there are 12. Telephone numbers even with the "1" and area code, only have 11 numbers. (01:01:10)
Other mistake: In the scene where Max is all beaten up, Machine slashes his throat and you can clearly see that the knife's blade is dull, because there's no cut or blood. (01:21:55)
Answer: Machine first rips off the tape then slits his throat with a knife he had hidden. If you put the movie in slow play, you will see what I mean.