Limited range of motion on one side could cause some deviations in scapulohumeral rhythm, so your force application won't be optimal and may cause injuries, or even cause uneveness and side effects in gait cycle. And with time it tends to get worse since the body would be trying to adopt to execute the function. But suboptimal force application eventually would cause joint injuries if a convex (humerus) is rolling without gliding or vice versa or doing it in suboptimal rhythm.

That's my personal take, not a doctor, study kinesiology as a hobby.

All such minor mobility issues could be addressed by body conditioning excercises including simple isolated mobility drills to learn range of motion of joints.