Eagle-Eye Detection

Used in mystery-themed media, where a detective relies on observation of otherwise-unnoticed clues at a crime scene, or discrepancies in witnesses' or suspects' testimony, in order to solve the mystery.

May be related to Awesomeness By Analysis, but in this case the sleuth does not necessarily have to be of genius-level intellect; he/she just needs to be able to pay keen attention to detail and to be able to sift critical information away from irrelevant or unimportant information. It is usually Taught By Experience, and subverts Your Eyes Can Deceive You if the detective knows to look past what is on the surface and seek out the facts, and only the facts. For this trope, Did Not Do the Research is not a viable option, or else the investigator will come across as incompetent.

Unlike Sherlock Scan, the detective will generally refrain from making (or attempting to make) guesses about a person or situation upon seeing them for the first time; nor can he/she afford to make on-the-spot assumptions about the person, as they may turn out to be false. Instead, if observations are made while interviewing a person, questions may (and in some cases, should) be asked, and checks are then made to confirm or refute the claims that are made.

Also, unlike Hyper Awareness (which is often used only as a humor-themed gag or for one-time plot purposes), Eagle Eye Detection is much more realistic and is a constant trait of skilled detectives and investigators. If Hyper Awareness is present in the work in question, it is toned down to a bare minimum, or at the most reduced to realistic levels, so that the viewer (or player in a video game) can learn at the same pace as the fictional protagonist(s).

Once a clue is sighted that may be crucial to solving the case, though, it is not immediately discarded or let go of; the burden then falls on the detective to compare/contrast that clue with other gathered evidence and see how it relates to a suspect's guilt, in order to make their case.

Compare and contrast Hyper Awareness. Contrast Sherlock Scan.

The trope name comes from the 1993-94 PC game series Eagle Eye Mysteries, a detective-themed Edutainment Game series; in particular, the second game had a feature where the glowing boxes that usually denoted witnesses or clues could be turned off, forcing the player to be that much more observant of the scenery in looking for clues. The series itself also required the player to select the best clues that told the facts, proved or disproved witness statements, and generally painted a plausible picture of what happened and why.

Not related to Eagle Eye, the 2008 movie.

Examples of Eagle-Eye Detection include:

Film

In The Pelican Brief (based on the novel of the same name), the titular document was formed due to Darby Shaw's (played by Julia Roberts) investigations based on a theory she came up with regarding the assassination of two Supreme Court judges. To form the brief, she researched the dead judges' case records and kept an eye open for any traits the two men may have had in common.
In Sleepy Hollow, this is Ichabod Crane's preferred method of solving the mysterious murders in the titular village. He uses revolutionary (for the time period) methods of investigation, including autopsies of dead bodies, and scoffs at the supernatural explanations the residents come up with (due to his own Harmful to Minors childhood memories of his Sinister Minister father). The supernatural explanations turn out to be true.
Used to investigate the Jack the Ripper killings in From Hell.
Hot Fuzz: Nicholas Angel uses this to come up with a very wordy but otherwise plausible theory about the ~~murders~~ accidents taking place in Sandford, centering around (he thinks) a lucrative property deal. Turns out the murders are for a much more mundane reason - keeping up Sandford's level of perfection.
Plays a role in Detective Spooner's murder investigation in I Robot.
In National Treasure, it becomes an important skill for the protagonists to advance through the plot.

Live Action TV

Frequently happens in the Law and Order series, especially the first incarnation.
CSI and its various incarnations, with the detective work taking place mostly in the crime lab.
Happens in every episode of Murder, She Wrote, with each mystery solved by Jessica Fletcher outlining a visual clue that was shown earlier in the episode, and a clip of said visual clue playing back for exposition.
Featured during the investigative portions of The Good Wife.
Takes place in the lawyer drama series Close To Home.
Shown often in The Closer.
Without a Trace: Investigations in each episode depend on this.
Used in the 1991 series Silk Stalkings to investigate upper-class sex-themed crimes.
NCIS had this in its first incarnation, mostly inside the forensics lab or the autopsy room.

Video Games

A necessary tool in the Phoenix Wright: Ace Attorney series.
The Eagle Eye Mysteries series, as noted above.
Could be considered an in-universe example in L.A. Noire, where L.A.P.D. Detective Cole Phelps is known within the department for being a better-than-average detective, ostensibly because of this ability.

Board Games

A necessary skill in Clue.

Comic Books

This is one of The Question's most well-known traits. Next to his wild and crazy conspiracy theories, of course.
Batman employs this in his investigation of criminals, doing background research and analyzing clues to get information on the case at hand.
In The Flash, during the "Death of Iris Allen" story arc, Barry discovered that the supposed murderer, Clive Yorkin, may not in fact have been responsible for Iris's death, and so he did some crime scene investigating, including examination of security camera footage. Turns out it was Professor Zoom who killed Iris at super-speed while going fast enough to be virtually invisible to recording security cameras and thus frame Yorkin for the deed. (Then it turned out Iris was Not Quite Dead.)
The Martian Manhunter did this often in his human guise as a private investigator, when he wasn't using his powers.

Literature

Agatha Christie's character Hercule Poirot may be the Ur Example, or a candidate thereof.
Plays a role in The Hardy Boys and Nancy Drew mysteries.
The children's book series The Puzzle Club, and the animated series based on it, is about a trio of children who solve mysteries this way.
Several Encyclopedia Brown mysteries are solved this way.
Sherlock Holmes himself did this in many of his early cases. A Study in Scarlet, for instance, devotes a couple of pages to his careful inspection of the scene of the crime and his picking up on details that didn't catch the attention of the police. Also, the short story Silver Blaze required that he visit the two separate crime scenes to collect evidence in order to make his case.
The Retrieval Artist series of sci-fi detective novels has Noelle DeRicci, a detective with the Armstrong lunar police force, whose ability at decipering crime scenes compares favorably with that of any TV CSI. Pity that she's often the Only Sane Woman on the scene.

Web Original

Online text-based game Sleuth relies on the player to pay attention to all clues and witness statements using this trope.

Western Animation

Velma is well-known for this, in every incarnation of her character.
During the Justice League Unlimited episode "Flash and Substance," Wally West is seen in his crime scene lab running tests on a bloodstained shoe, which was cleaned off with dish-washing soap. He informs his supervisor that his investigations have revealed that the soap is the same type as the brand that was found in the murder victim's kitchen.
During the Superman: The Animated Series episode "The Late Mr. Kent," Clark had to use his investigative reporter skills to collect enough evidence to exonerate an innocent man on death row.
There's also Batman: The Animated Series and its tie-in movies. Played especially strongly in Batman: Mask of the Phantasm.

Real Life

Crime scene investigators and detectives have to pay attention to every detail of a case, in order to build convincing evidence for/against a suspect. All aspects of the evidence have to make sense and be able to stand up in a court of law. Anyone who has spend enough time in court (as part of their work, that is), will have had enough opportunity to observe trial proceedings and see how different pieces of evidence have to come together to build a case for/against a defendant.
On the fun side, this plays a role in murder mystery-themed parties.