I was actually just talking to a friend about this the other day. Well, specifically we were talking about how to get away with a crime (that sounded shady) lol. If looking at murder cases:
The first mistake a criminal can make is killing someone they know. You see it numerous times....the husband who kills his wife, or the woman who kills son etc. The problem is, when a person dies, the immediate family become the primary suspects along with lovers(partners), friends, and coworkers. This is why serial killers are so successful. They kill random people.
The second mistake is leaving evidence behind. Wear gloves so no fingerprints are left behind and a shower cap to keep your hair from falling out onto the crime scene. DNA is everywhere!
The third mistake is not doing research. If you're going to commit a murder, make your approach in an area where there are no witnesses or video cameras.
The fourth mistake is carelessness in planning. If you need to buy supplies for the murder, do so in cash, and once again, do so at a store that does not have video cameras pointing at your face. They exist, they're just hard to find.
The fifth and final mistake is.... committing the crime! Just don't do it! Most likely, you're going to get caught....plus it's not nice! :)