The main character in most murder mysteries is the detective: the one in search of the killer. Here, as nowhere else, the clammy fingers of stereotype have a way of throttling the mystery genre dead. Make sure your detective stays away from clichés--the rumpled gumshoe with the trenchcoat and fedora, the eccentric old English lady who solves murders over tea and so on. Raymond Chandler perfected the former, Agatha Christie the latter; no matter how good a writer you are, you aren't going to top their efforts. Look for ways to make your hero original. Maybe he's not even a full-time detective, but rather a musician or someone with only tangential connection to crime-solving. The more imagination you invest in your hero, the more willing the reader will be to follow you. The same rules apply to the killer: he should be someone interesting and original, devoid of cliché.
One of the joys of murder mysteries is trying to guess who did it before the big reveal at the end. As the author, you have a sacred duty to respect that. While you should do your best to hide the killer's identity, leave genuine clues that a clever reader can conceivably piece together, and stay away from arbitrary twists or other ways of "cheating." The line can be surprisingly blurry at times. For instance, it's perfectly acceptable to use a red herring, or evidence which points away from the killer, but it's not acceptable to introduce new evidence at the last minute that changes the entire equation, or reveal information in a flashback that later turns out to be false. Think about how you might feel if you were reading your mystery, and whether you'd consider a given device or development "cheating."
Many of the clues and details of a murder mystery hang on actual forensic evidence--things like fingerprints, gunpowder residue and the way mud leaves tracks on the floor. If these details don't ring true in your book, the whole mystery will fall apart. Take some time before you write to familiarize yourself with forensics, residual evidence, and the nuts and bolts of any clues on which your tale hinges. It needn't be overtly technical, it just needs to stick to the facts. A number of excellent reference books have been written on the subject, including "Scene of the Crime" by Anne Wingate, and "Modus Operandi" by Mauro V. Corvasce and Joseph R. Paglino (see Resources).