When Dexter first leans in to view the body of his "father" at the morgue, the clock behind reads 4:11. The camera cuts back to the face and glides back up to Dexter's with the clock now reading 4:17. A few shots later, the clock is seen as 4:01.
When Dexter is receiving the notification in the office, an extra in a black shirt is standing at a counter in the background. In the next shot, he is walking to the counter where he just was.
When Dexter is putting the trash in front of a neighbor's house, he goes to put the lid on the trash can, but in the next shot the lid is missing entirely. It's not in his hand, nor is it on the can.
The medical personnel in Dexter's childhood flashback reveal that his blood type is AB-. He goes on to state that "it's hard to come by, and our supply was low." While it is correct that type AB- is the rarest blood type, at around 1% frequency in the US, a person with AB- blood can receive a blood transfusion from donor blood of types AB-, A-, B-, and 0-, making it a preferable blood type to have for a person on the receiving end of a transfusion.
While in Dexter's biological father's house, Rudy puts on the album "Fire and Water" by the band Free, as seen by the album cover as well as the record label. However, the song heard is Foghat's "Slow Ride". Same mistake is repeated later when Dexter puts on the same record in his apartment, this time Creedence Clearwater Revival's "Have You Ever Seen the Rain?" is heard instead.
When Debra is lying in bed 'naked' after her boyfriend is playing with the scissors, she leans to one side and you can clearly see that she has tape on her breasts.
When Angel is turning around on the bridge, he stops halfway through his turn, backs up, and then continues. From the view of the car, he could have easily completed the turn without backing up as there was a lot of space. The K-turn was completely unneeded.
When Angel and Doakes are driving over a bridge, they spot a suspect walking the other direction. When Doakes gets out and confronts him, the suspect darts, causing Angel to turn the car around and pursuit him. As Angel is turning around, there's a wide shot of the suspect with Angel in the background. In the further background, there are clearly road closure signs blocking off the bridge, this is how crews close-off sets that are filmed in public.
Dexter states that his biological father lived "five hours up I-95." However, Dade City is located in Pasco County, on the western side of Florida, and would actually be five hours up Interstate 75, which also runs out of Miami, but actually travels up the western side of the state where Dade City would be located.