Let's assume you use big heliostats and can punch holes in the wall that range from fist-sized to dinner-plate sized. You watched The Mummy, right?
The Mummy, 1999, with heliostats as imagined by the director.
This scene imagines lighting up a whole underground room with a single beam of sunlight. While impractical, it could probably be made to work...for about five minutes as the sunbeam coming from the ceiling of the underground tomb walked along the floor. The practical difficulties of using mirrors to light things are:
*Practical light paths
*Optical limits
*Many single-failure points that cripple the design
*Houses are not built to be lit
*Tough to do with realistically-sized optics
*Real gain?
The advantages are:
*You could probably use a single 100W short-arc lamp for your whole house
*One bulb to change
Practically speaking, a perfectly clean, vapor-deposited mirror reflects 98-99% of the light that hits it. However, keeping them dust-free is difficult. You could put a car-HID projector bulb in a closet with small mirrors bouncing light around the house, and put diffusers of various sizes in the beam-path to scatter some light into the room. Keeping them all aligned would be tough. Start small:
Find the longest straight path through your house. Get a $10 "Flood To Throw" zoomy light and point it along that path. I suggest using a camera tripod, or duct-tape to the back of a chair. Now put a mirror along this path to shine the fully-focused light where you'll want more light, then start putting a diffuser in the beam path. There are limits with this rough-draft, notably that you may walk through the beam path or intercept it with your eyes. How well does it work?
Most people like diffused light. Near-perfect room light for me is up-aimed LEDs on heat-sink conductive trim around the room. This gives minimum glare, but isn't terribly efficient - not that I care. I don't like counting watts, I like living. What are the efficiency gains in a single-source light? Not much. To decently light a house takes watts and watts, especially if you can't dim fixtures for task lighting.
So:
If you can make a beam path by putting up scads of mirrors or punching holes in walls, it could work. It's kind of crazy, and you'll see all the spiderwebs in those corners. Make sure you plot the concept out well.
Note: This is only one step from using a heliostat outside a window to get daylight all day.