Factual error: When Costigan takes the Dr. Smith-prescribed Oxycontin tablets, the tablets are incorrectly shown as large, white oblong pills with the prescription bottle just labeled 'Oxycontin'. In reality oxycontin tablets are small, round, various colored pills (dependent on mg dose) with the dosage number (in mg) imprinted on one side of the tablet as 10, 15, 20, 30, 40, 60, 80, and 160 (I believe 160 mg tabs are discontinued) and the opposite side imprinted as OC or OP. Also, the dose (in mg) would have been printed on the front bottle label.
Suggested correction: She doesn't give him oxytocin. She gives him antidepressants. Also, medication is not uniform, different companies make medicine in different forms.
Continuity mistake: When Costello lies dead in the shovel of the excavator, his right arm moves between shots. (First it is up - in the far shot, it is down).
Continuity mistake: In the restaurant, after Costigan says "School is out," he starts to bring the cigarette to his mouth, but before he smokes, while the action, music and dialogue continues, the shot cuts to him already exhaling the smoke.
Continuity mistake: When French is holding the bag with the hand he places a ring very close to Costello's cheek. A second later, without him having moved, the hand is at jaw level and farther away.