Continuity mistake: Dexter goes to the morgue to see the body of his father. When he first sees the body, he bends down, and the clock behind him reads 4:11. A moment later when he stands back up the clock is at 4:17. A couple of minutes later the clock is at 4:01.
Other mistake: Doaks says he saw the man's gun and chased him, lots of questions arise about what happened, but no-one mentions how a cop has no right to ask a person about a gun they have on them without probable cause. Doaks has no reason to even go after the guy.
Suggested correction: Florida is not an open carry state, so if the man was displaying a gun, the cop had probable cause to pursue and question. Even if the man had a permit to carry a weapon, per Florida law, that weapon must remain concealed. If the cop could see the gun, it was a violation of the law and the cop could not only question, but arrest him.
Seeing Red - S1-E10
Visible crew/equipment: When Dexter is walking towards the entrance of the Marina View Hotel to examine the crime scene, a boom mic is visible in the glass of the window on the right. (00:07:35)
Seeing Red - S1-E10
Continuity mistake: When Angel is at the bar, the girl he is talking to has a drink held up by her face when viewed from behind. In every shot from in front, the drink is on the table.
Continuity mistake: When Rudy has Debra in a headlock on the yacht, his left hand continuously moves between shots from on her head to gesturing in the air.
Revealing mistake: In the scene where Rudy's body is found by the police, you can see Rudy breathing and his pulse in his neck. (00:51:05)
Continuity mistake: When Rita is talking to Bob outside the house, she is carrying a box. A piece of tinsel keeps moving from hanging over the edge of the box, to being tucked inside.