Check for any lose bricks or cracks in the firebox, which is the area where you actually build your fire. Even with a gas fireplace or combination gas and wood be sure to check this area at least once a year. Flammable surfaces should never be exposed to the coals or flames.
Water can sometimes leak into the chimney through the crown, which is the area where the concrete from around the chimney meets the roof area. If this happens it can lead to rusting and water damage in the chimney pipes and can even lead to chimney fires where the material becomes brittle and damaged along the chimney.