Plot hole: In order to elude Elway at the airport, Dexter fills a backpack with random items and leaves it unattended under a seat, and then tells a desk clerk that he saw Elway deliberately put the backpack there and walk away, which leads to security detaining Elway and the airport being evacuated. Airports have security cameras everywhere, so security would have reviewed the footage and seen Dexter was the one who placed the bag there. They then would have gone through all security footage since he entered the airport in order to deduce his identity and then located and arrested him.
Plot hole: A couple episodes prior, Deputy Marshal Clayton stated that he shared Hannah's picture everywhere after receiving a tip that she may be in Miami. In the same episode, Hannah was spotted at a hospital and Clayton was called in about it. This should have only increased public awareness concerning her, but at the beginning of this episode, she somehow made it through airport security and all the way to her gate before spotting Elway and hiding from him in the ladies room.
Other mistake: The marriage certificate for Rita's first marriage shows her date of birth as 04-19-1989 and Dexter states she married at 16. The marriage date is 08-16-1989, when she would have been 4 months old. She also would only be 17 at the start of the series (2006) if she was born in 1989. (00:13:45)
Factual error: When Dexter and Doakes are looking at the severed foot wearing a soccer cleat, Dexter states, "The foot was severed between the tarsus and the metatarsus." However, the foot was severed proximal to the tarsus, through the tibia and fibula. The cut was easily too high to be between the tarsus and metatarsus. (00:16:45)
Continuity mistake: In Season 3, Episode 2 during a conversation with Miguel's wife Sylvia, (Syl), and Rita in a kitchen, Syl says that they don't have any children after trying. In this episode, Syl is trying to help Dexter sell his condo and says that she downsized and focused more on "the kids."
Continuity mistake: When Doakes is about to be killed by Guerrero, the police save him by shooting Guerrero, giving him a bullet wound on his right shoulder. He is also cuffed on the ground to be arrested. However, when he is pulled up, Guerrero does not have a bullet wound anymore.
Audio problem: When Deb tells Angel to "look up" warning him of the security camera, Angel moves his lips as though he's talking but there is no audible dialogue. A few seconds later, his lips stop moving but then his audible lines are spoken. Then, again, there is no dialogue, but his lips move again. (00:07:15)
Continuity mistake: When Dexter started removing the plastic off Travis' body, his small knife was stabbed into the chest, but during that, the sword was already stabbed into the chest, not the knife, and then again, he removed the knife from the body, and then stabbed him with the sword. (00:12:05)
Factual error: When Dexter is in the hospital as a child, the doctor says that Dexter has a very rare blood type, AB negative. Although it's very rare, the people with AB- can receive donor blood with A-, B-, AB- and 0-. AB- is a very good blood-type when you need to receive blood. While it is true that hospitals normally have to use AB- because of the complexity of other proteins (and to prevent adverse reactions), in case of an emergency, like Dexter's, and a shortage, a hospital will use a blood type close enough to not likely cause a reaction. In this situation, the hospital would give Dexter O-, B-, or A- instead as blood loss would normally kill a patient long before a suitable donor could be located, called in, admitted to the hospital, and have the transfusion set up. (00:31:00 - 00:32:00)
Factual error: In The Beginning while Dexter is on his boat in Miami, you suddenly see mountains in the background, of which there are none in Miami. Also the palms are too high, indicating they are from California. And the worst setting mistake is the Florida tags in front of the cars. Only commercial vehicles have front tags.