Continuity mistake: When Sydney and Danny are at the pumps outside the city talking about her job, between front and back shots the hair at Sydney's left ear changes position from stray strands blowing in the wind to neatly tied back - no stray strands. (00:18:50)
Continuity mistake: In the parking garage, after Sydney knocks the machine pistol out of the hit man's hands, it lands with the barrel pointing away from The Two of them and remains in that position during their entire fight. When Sydney grabs it off the ground, the barrel is pointing toward them. (00:43:30 - 00:44:10)
Continuity mistake: After Sydney learns that SD-6 is not part of the CIA, she goes to Taipei. Just after she arrives, she takes a man's car. At this point the number plate reads DH 5578, but, in the next shot, as she is driving away, it is JU 1587. (00:51:15)
Continuity mistake: When Sydney is tortured, she loses some teeth and a stream of blood flows out the right side of her mouth. When she returns to SD-6 and speaks with the director, the blood is gone (fair enough). Outside on the street in the following shot, the blood has returned, but there's no reason to believe that she is still bleeding. (00:58:40)
Continuity mistake: When Sydney takes Danny upstairs, her hair is tucked behind her ear. When she turns to face him, her hair is no longer tucked behind her ear.
Answer: Bad Day by R.E.M.