Revealing mistake: When Lazare shows up to talk to Will, we see that his left hand has been cut off. When Lazare is about to leave, he has his hands at his sides, and we can see that both arms are the same length, but the left one should be shorter, because it has no hand.
Revealing mistake: When Syd's Dad rescues her in the car park, he starts shooting at the other car. After firing one shot the slide of his gun locks back (indicating it's out of bullets), but when the angle changes he carries on firing with no problems. (00:43:20)
Revealing mistake: When Sydney and her father go into the office to talk, the office doors begin to close before Sydney uses the remote to close them. (00:13:00)
Revealing mistake: During the episode "Double Agent", Sydney and Vaughn are at her apartment, cooking dinner. Sydney reaches into the "hot" oven, without an oven mitt on.
Answer: Bad Day by R.E.M.