IMO the most common mistake is pulling with the arms. The explosive pull should come from the traps, ankles, and hips. I found the best way to correct this for myself was to start off with "scarecrow" cleans, then progress to dead hang cleans, then progress to hang cleans. In a scarecrow clean, you pull the weight in a controlled fashion to the lower chest, then practice whipping your arms around to pull yourself under the bar. In a dead hang clean, you eliminate the hip movement. Once you've mastered these, hang cleans shouldn't be a problem.
The second most common mistake IMO is receiving the bar improperly. I see so many people who catch the weight with their arms way too low - you really have to get your elbows high and form a shelf for the weight. Work on wrist/tricep flexibility as it seems a lot of people are lacking in this and it's obvious when they do any sort of cleans. Doing front squats with a "clean grip" helped me with this.
Third problem is "donkey kicking", kicking up the feet after the explosive pull. Good positioning of the feet is essential to a good/safe clean, so this is a no no. Your feet should start at about hip width and after the explosive pull they should end at about shoulder width.
