Continuity mistake: After Costello smashes Costigan's wrist he hands all of the dollars he has in his right hand. A frame later money reappears in the hand.
Continuity mistake: When a shootout between Sullivan's men and Costello's starts after Queenan's death, one shot initially hits the left glass of the van, then in the next shot the glass is intact, only to be hit again.
Visible crew/equipment: When Queenan dies after being thrown out of the building and his body is crushed on the ground in front of Costigan, as he looks at his hand covered in blood, in the shot on the top on the left side of the screen the dolly track of the camera is visible for a second.
Answer: The FBI and police are separate organizations that do not share full information. Only the FBI and Costello himself knew about the informing, and the FBI can only do so much to stop Costello being caught without drawing attention to their relationship. The police and Costello's gang are fighting a separate battle, hence the two moles.