Dips can certainly cause shoulder impingement, but learning proper form and pacing yourself in regard to weight can minimize your chances of injury. Dips can work your triceps, shoulders, chest and back, depending upon which variation you use, but the stress on your shoulders is constant. Performing the move properly puts more stress on your muscles and less on your joints.
Shoulder impingement is a condition where your shoulder blade presses on the surface of your rotator cuff, causing pain and inflammation. The pain gets worse when you lift your arm, or in the case of dips, when you lower yourself toward the ground. If you find your elbows moving away from your body during dips, you are putting yourself in prime position for a shoulder impingement. Most cases don't require surgery but can still keep you from your workout for several weeks.
Too Much Weight
If you've been doing dips for awhile and have recently progressed to bodyweight-plus exercises, adding too much weight too soon makes you a candidate for shoulder impingement. As exciting as it is to strap that plate to the weight belt, you can easily put too much stress on your upper body before your muscles are strong enough to handle it. When your muscles can't hold the load, part of the stress is transferred to your shoulder joint, which is not designed to bear so much weight in an up-and-down position. When you combine the extra weight with the poor form you fall into while you struggle, you can't expect your rotator cuff to come out unscathed. Increase your weight very gradually instead, and use a smaller range of motion until you are comfortable with each progression.
Dips look simple, and some people tend to just jump onto the parallel bars and begin without instruction. The reality is that you must be very careful in your technique if you hope to avoid injury. The bars should be shoulder-width apart, but never more than 5 inches from your hips, to avoid stressing the shoulders. When you dip, you should only feel a slight stretch in the shoulders, and your elbows should be bent around 90 degrees. Your body should be straight, even if you must bend your legs to keep them off the ground. This holds true whether you lean forward to work the chest or keep your elbows close to work the triceps -- if you can't do the exercise with proper form, you're not ready to do the exercise.
If you've had a previous shoulder injury, avoid dips altogether. Instead, do presses and extensions to work the same muscles that dips would work. If you've had shoulder impingement, a rotator cuff injury, tendinitis, bursitis or a similar injury, your shoulder is likely in a weakened state, even if it has healed. It may be less able to handle the weight of your body in a semi-rotational motion, and you could re-injure it more easily. If dips are important to you, consult your doctor to get the all-clear before you attempt the exercise.