One of the biggest mistakes people make on any pushup is to not maintain a co-con-traction of the upper back muscles while descending on the pushup.
This is when your back rounds forward and your elbows flare out at 90 degrees from the shoulders as the rest of the body rises.
What is correct is having your elbows at 45 degrees from the shoulders and as you descend into the pushup your shoulders are down and retract together. As the body rises your shoulder blades return to a neutral position.
The problem is this movement mistake often results in wear and tear to the rotator cuff and reduces the toning effects of the exercise at your chest and abdominal area.
Damage to these muscles, and your ability to do many upper body exercises may be compromised.
If you are not strong enough to stabilize the shoulder when doing the exercise on the floor, then you need to start in an incline position and slowly reduce the incline until you are able to accomplish it on the floor.