Whenever I teach and coach the press at seminars, the same faults show up.
1. Grip width
2. Wrist position
3. Elbow/shoulder position
It’s a little difficult to discuss this without a visual aid, so I made an explanation video below after a press workout. Starting Strength does a good job explaining grip width, but for some reason people usually use too wide of a grip. I first wrote about proper wrist position on the SS forums in 2009, and it still is a common fault. Basically the bar needs to be over the heel of the palm instead of back in the hand or fingers. Lastly, over the last couple of years I’ve put more of an emphasis on maintaining proper external rotation during the press as it will distribute the force application through the full muscle bellies of the triceps and anterior deltoid. If these three flaws are present, then it will inhibit press progress. If you are doing these three things wrong, then it will behoove you to accumulate several weeks of work with lighter loads to develop and train the musculature through proper mechanics and range of motion.
Other pressing related sources:
Better Push-Ups video, external rotations role in push-ups and benching
The Lats While Benching article, discussing the anatomy of external rotation during benching
Internal Rotation Post, showing some MWOD fixes for internal rotation
Pressing a Dead Horse post, talking about some programming, but general methods of improving the press.