When Dexter and Deb are in the ambulance talking, the ring on Deb's left hand jumps between her ring and middle fingers.
Dexter finds the story of Laura's murder in the October 3rd edition of the newspaper. The October 3rd paper would report on what happened October 2nd. Brian would have known that they were actually "born free" on 10/2, not 10/3 (leaving aside the fact that if they were found on 10/2, then the murders actually occurred on 9/30).
Brian Moser picks the lock to access Dexter's apartment door, which appears to be an appropriate lock-picking technique and tools. However, the tension wrench does not rotate the cylinder when the pins have been picked; the cylinder stays in the locked position.
When searching Rudy's apartment, Dexter goes over to look at the Barbie record player. The African-American police employee who is cataloging the items is clearly wearing a laminate with a photo of a bearded, white, middle-aged man on it.
Inmates have to call collect on a recorded line. There's no way Paul could call Rita as often or easily as he repeatedly does.