What causes a slight leg length discrepancy?

Multiple reasons: One can be born with a short leg. Most of us have one leg, foot, arm slightly shorter than the other by a 1/4" or less. Injuries can cause a short leg such as breaking a leg and it heals shorter than the other. Muscle spasms can cause the hip to tilt and results in a short leg. I would see a podiatrist or orthopaedic doctor. Long term, a short leg can casue a lot of foot, leg, hip, low back pain.