Shoulder flexion is going to be the biggest limitation in athlete's muscle-up mobility. We use the back to wall shoulder flexion test to isolate the shoulders and prevent compensations with the spine. Pay close attention to hand position and to not let your elbows bend during the test.
Shoulder extension is a huge component of solid mechanics for the dip component of the muscle-up. Without sufficient shoulder extension mobility, athletes will have a difficult time maintaining proper form, and we often see discomfort in the front of the shoulder when extension range of motion is reduced.
The thoracic spine (upper back) is another commonly limited mobility area. This can impact the low back, neck, shoulders, and limit your overhead mobility.
Good kipping requires the ability to open the upper back up.
In kipping, we want to move into a globally extended arch position with the shoulders, upper back, and hips extended.
For athletes with tight hip flexors, we'll often so the legs separate, and the athlete loses tension that reduces their efficiency of movement.