The song played in the beginning and at the end of the episode (the theme) is El Diablo En El Ojo by Tindersticks.
Goof: Tommy receives a phone call at 12:17 am from the local police station telling him to come pick up Eileen. When Tommy arrives at the police station, an officer asks him what was Eileen doing running in the woods at two o'clock in the morning. If Tommy was called after Eileen was taken into custody, the time on the clock was very wrong.
The song in the end of the episode is
Things Have Changed by Bob Dylan
While the union guys are looking for one of the molars that they dropped on the floor while dismembering a body, you can see the body on the table take a deep breath. The body is supposed to be already dead.