The initial murder occurs during an solar eclipse, which must occur on a new moon. A couple days later, a full moon is shown. This would have to be two weeks later.
Solar eclipses are rare and usually highly publicized events, yet this one seems to have taken everyone by surprise. Their occurrence is highly predictable - the date, time and location of every eclipse, whether lunar or solar, total or partial, for the 21st century, is known. Typically, on a public open area such as a beach, there are observers using the proper apparatus to safely view the event. Furthermore, the last total solar eclipse visible in the southeast US was 7 March 1970; the next total eclipse to be visible in the southern US is on 12 August 12 2045.
The depiction of the eclipse is inaccurate in several ways. From the beginning of the eclipse, it takes only about a minute or two for the moon to completely block the sun, whereas in an actual total solar eclipse, it takes well over an hour. The behavior of the shadows as depicted is nothing like what shadows do during an actual eclipse. Several features of an actual total solar eclipse, such as the "diamond ring" effect, are absent.
The boy at the end of the episode shown playing Xbox 360 is just mashing buttons. Xbox 360 controller in the boy's hands has 4 green lights flashing. Four green flashing lights on an Xbox 360 controller means that the controller itself is turned on, but the console is not connected to a power source.
The ambulance that is transporting medical examiner Alexx Woods is apparently equipped with Fire Engine air horns, but none are visible above the cab or in the bumper.
Horatio and Delko were in the criminal's home and looking through the telescope. One time Delko put his eye on the eyepiece to the telescope and Horatio pressed the button to move it to the next location. That would most likely interfere with the movement of the telescope.
During the solar eclipse everyone looks up at the eclipse without any eye protection, during a solar eclipse if you don't protect your eyes with something you cause retina damage
When Erik and Horatio are in the upper apartment and realize that they can see the fourth victim through the telescope, they re-draw their side arms and leave the room in a hurry. They need to go down to the lobby of that building, then over across the street to the dorm rooms, then up to the dorm room. It makes no sense for them to have their weapons drawn that entire time.