A modern, properly installed fireplace should not require a mantle to catch smoke; they are purely decorative. I believe Nathan was referring to the glass doors and metal screen that an indoor fireplace does require to be safe. Also that the inspector may have been referring to the surround (protects the walls around the fireplace and is often topped by a decorative mantel); the masonry directly adjacent the fireplace, on the walls and including a section of the floor.
The white mantle is decorative. The exposed hearth and the tile surround are functional.
In order to lower the risk when using your fireplace, you should:
Keep all combustibles a safe distance away from the hearth.
Use a fire screen to prevent sparks.
Install a spark arrester at the top of the flue to guard against roof fires.
Keep a fire extinguisher handy.
Install smoke detectors on every level of your home. You should also have a carbon monoxide detector.
Code -rumford.com (note, masonry fireplace; for steel-box construction consult the manufacturer)
R1001.11 Fireplace clearance. All wood beams, joists, studs and other combustible material shall have a clearance of not less than 2 inches (51 mm) from the front faces and sides of masonry fireplaces and not less than 4 inches (102 mm) from the back faces of masonry fireplaces. The air space shall not be filled, except to provide fire blocking in accordance with Section R1003.13.
When masonry fireplaces are part of masonry or concrete walls, combustible materials shall not be in contact with the masonry or concrete walls less than 12 inches (305 mm)from the inside surface of the nearest firebox lining.
Exposed combustible trim and the edges of sheathing materials such as wood siding, flooring and drywall shall be permitted to abut the masonry fireplace side walls and hearth extension in accordance with Figure R1003.12, provided such combustible trim or sheathing is a minimum of 12 inches (305 mm) from the inside surface of the nearest firebox lining.
Exposed combustible mantels or trim may be placed directly on the masonry fireplace front surrounding the fireplace opening providing such combustible materials shall not be placed within 6 inches (152 mm) of a fireplace opening. Combustible material within 12 inches (306 mm) of the fireplace opening shall not project more than 1/8 inch (3.2 mm) for each 1-inch (25.4 mm) distance from such an opening.
Under my interpretation of #4, the mantle pictured is to close to the edge of the fireplace (~8") to stick out so far (~4"). It isn't the best picture to show a safe fireplace. Merely, it does a good job showing a useless mantle. It lacks doors and a screen but at least they attempted to keep combustibles (drywall) one foot from the opening in every direction.