Dirty Harry - S4-E5
Continuity mistake: When Dexter listens to Officer Lundy's tape recording, we hear Lundy say that the Trinity killer's weight is 190 to 200 pounds. When we saw him recording that, he said 200 to 220 pounds.
Visible crew/equipment: When they are at the crime scene, you can plainly see the camera and camera man reflected in Special Agent Lundy's sunglasses several times. When it is a close up shot, it is even more obvious.
Revealing mistake: When Dexter is retrieving a blood sample after cutting Benny Gomez's cheek, there is no blood in the dropper and he puts no blood on the actual slide. (00:49:50)
Factual error: In the newspaper article from the Trinity killers past - the report states that someone called 911 and dispatch gave them instructions. The death occurred in 1959. The first 911 call was made in 1968. (00:39:24)
The Getaway - S4-E12
Plot hole: If we assume that Dexter took off the oil cap while it was still in the shop for Arthur, it still doesn't explain how Dexter got the jump on him when his car (hours later) broke down. Arthur's not shown to stop, but to merely drive for hours on end until night. Arthur's on a barren strip of road with no other cars or traffic to be seen for miles. It cuts from Arthur looking in his engine to Dexter suddenly walking out from behind the Mustang. The only explanation is that Dexter waited in the car with Arthur, which doesn't make very much sense. All this takes place in the last 15 minutes of the finale.
Suggested correction: Dexter was hiding in the trunk of the car. If you look very closely when Arthur is saying "Where's my f***ing oil cap?", you can see Dexter's leg appear to the left (viewer's right) of the rear passenger side tire, in the open space under the car's body.
The trunk thing makes sense, but they could have made it more clear. I too was wondering how the heck he just appeared seemingly out of nowhere.
No disagreement there. I had to watch the sequence a few times to notice it, because it definitely looks like he climbs out of the back seat. I guess they felt having both characters in shot from that angle worked the best, as opposed to using several cuts.

Continuity mistake: When Dexter is killing Stan Beaudry, the drop of Beaudry's blood encompasses the width of the blood slide when the two pieces of the slide are pressed together, but then goes to being roughly half the size when the shot changes.
Slack Tide - S4-E7
Other mistake: When Dexter shreds Laura Moser's file, he actually shreds a file for Estrella Carazo. (00:32:57)
Dirty Harry - S4-E5
Other mistake: When Lundy is shot and falls to the ground, there is no visible injury even though he is facing the camera. Later, Masuka says he was shot twice, once in the chest and once in the neck. The shooter was facing him. We should have seen the blood.
Dirty Harry - S4-E5
Visible crew/equipment: Before Debra is taken away in the ambulance Dexter is physically stopped from getting closer to the scene, and when Batista tells the cop that Dexter is one of them, in the next shot facing Dexter the reflection of the moving overhead boom mic can be seen on the car window. (00:04:05)
Revealing mistake: When Rita confronts Dexter about his accident being more than minor Rita turns the buggy with the baby in around to leave and it is clear the baby is fake. (00:38:20)
Continuity mistake: When Dexter and Masuka are discussing wanting to go home Dexter throws a can toward the bin and misses, landing by Masuka's chair. In the next shot as Masuka leans down to pick it up it is closer to the bin. (00:39:30)
Revealing mistake: When Deb is texting "Looks like it" to Anton, the buttons she presses on the keypad do not correlate with the message itself and the phone doesn't show any auto-correct feature being utilized, indicating that the text message was added in post production.
Other mistake: There's no way Arthur could have known Scott was 10 years old. In fact, it's highly likely he would not have known any of the boys he killed were 10 years old.
The Getaway - S4-E12
Other mistake: The tub Rita was found in was full of water, to the rim. Volume displacement dictates that when Arthur got out of the tub the water level would have dropped to well below the tub's rim.
Continuity mistake: When Dexter is packing kill tools for the road he "packs light" and chooses a knife and hammer. However once he's at the hotel room setting up the kill room he unrolls his entire set of tools like he does at all the other murder room scenes.
Dirty Harry - S4-E5
Visible crew/equipment: After the ambulance taking Deb to the hospital drives away, a crew member ducks down in front of a parked car in the background. (04:36:00)
The Getaway - S4-E12
Continuity mistake: The bathtub Rita is found deceased in is a standalone without a shower door, unlike previous episodes featuring the bathroom with a shower/tub with a sliding door. In a previous episode, Rita refers to the home as a "one-bathroom" house so it's not possible this was intended to be a second bathroom.
Suggested correction: The tub that Rita was found murdered in was in the home that Dexter and Rita purchased together after their marriage. The previous home in which the sliding glass door and "one bedroom house" comment was made was Rita's former home that she lived in with her husband Paul, not the home she purchased with Dexter after they married. They are two different houses.