1. Lack of control during the descent.
Lack of control can contribute to injury and prevent optimal strength gains. If you do not have control of your body during a pushup, you may find yourself in an awkward position which can result in injury. Lack of control will also inhibit progress by not consistently targeting the same muscles every time you do a pushup.
2. Not keeping the back, shoulders, core, and glutes tight.
Tightness equals stability. Keeping the back, shoulders, core and glutes tight provides a stable controlled platform to perform the pushup. Stability, along with control will reduce the chances of injury while doing a pushup and put you in the best position to perform pushups. You will be able to generate more force because the muscles groups are aligned properly and can work better together.
Stability in the pushup will look like a good plank at the top of the pushup. This tightness or flexing should be maintained throughout the entire movement.