Can you help explain what things CT scan often cannot show?

Depends on body part. If you look at the brain, for instance, ct can see a stroke, but MRI can see it sooner. In the shoulder ct looks at the bony structures well, but doesn't do so well looking at the labrum and tendons. In the lumbar spine, ct can see bony structure and spinal stenosis, but MRI is best for looking at disk herniation. These are just a few examples. Talk with your doctor or radiologist to make decision.
Ct scan. For an orthopedic injury a ct scan is great for showing any type of bone abnormality. It is not good for showing ligament, cartilage, or muscle damage. A MRI is better for those tissues.