As pointed out by others, luminaires above or near a tub/shower must be "steam-proof" (rated for damp locations). This means the fixture will be sealed in some way, to prevent moisture from entering the housing and causing damage and/or an unsafe environment.

NEC 2008
410.10 Luminaires in Specific Locations.
(D) Bathtub and Shower Areas. No parts of cord-connected luminaires, chain-, cable-, or cord-suspended luminaires, lighting track, pendants, or ceiling-suspended (paddle) fans shall be located within a zone measured 900 mm (3 ft) horizontally and 2.5 m (8 ft) vertically from the top of the bathtub rim or shower stall threshold. This zone is all encompassing and includes the space directly over the tub or shower stall. Luminaires located within the actual outside dimension of the bathtub or shower to a height of 2.5 m (8 ft) vertically from the top of the bathtub rim or shower threshold shall be marked for damp locations, or marked for wet locations where subject to shower spray.

Corrosion

The major concern here would be corrosion inside the fixture, which can lead to dangerous heating, arcing, shorting, etc.

Heat

Corrosion on contacts increases the resistance of the circuit, which can lead to excess heat, which in turn can lead to increased resistance. Given the right circumstances, wires/contacts can be heated to the point of ignition.

Arcing and Shorting

In some fixtures, contacts can be in very close quarters with each other. If corrosion builds up causing the gap between contacts to reduce enough, arcing can become a problem. Similarly, if the gap closes completely, a short can be created.

PITA

Corrosion in fixture can simply lead to a frustrating situation. If the screw base of a bulb becomes corroded enough, the bulb could become difficult or impossible to remove. This could lead to the fixture needing replacement, or at least an annoying bulb change experience.

Ground Faults

As we all know, water conducts electricity (in most cases). Because of this a deadly ground fault situation can be created, if luminairs are allowed to get excessively damp or wet. If enough moisture enters the fixture to cause dripping, a solid stream of conductive water could bring electricity within reach of a well grounded individual. In this scenario, a simple touch of the light could be deadly.

Minimum Code Requirement and the Problem with Uneven Lighting

It seems like you're trying to correct for what is likely minimum code requirement wiring. Usually that means a single electrical box for a light fixture in the middle of a room, or a switched outlet ostensibly for floor lamps. The problem with this minimal number of fixtures is twofold:

1. As you identified, there are entire parts of the room that will be in a shadow because light travels in a straight line. You'll get some reflections off of the walls and other objects in the room, but that will generally be at a loss on the order of 10x.

2. The intensity of light from a fixture that falls on an object is roughly proportionate to the inverse cube of the distance from the light. This means that an object 9 feet from the fixture has approximately 1/27 the light falling on it as does an object 3 feet from the fixture.

The above two problems can be summarized as uneven lighting. The trouble with uneven lighting is that your eye will adjust to some sort of average of the brightness. The single bright light in the middle of the room is probably way brighter than that average, so it becomes uncomfortably bright to have in your field of vision. At the other extreme, the shadows are likely much dimmer than average, so your eyes will likely just see dark.

Both of the above problems are lessened by increasing the number of light fixtures.

How Many Fixtures Do You Really Need? Experiment!

To achieve even lighting, you need way more fixtures than minimum code requirement. My last renovation included one light fixture for every 25 square feet on average which represents about 5 times the number of fixtures that were originally installed. That's just about what is minimally necessary if you want to avoid both shadows and having bright bulbs within your line of vision.

Of course, the ideal number of fixtures depends on your room shape, light fixture design, wall, ceiling, and floor colors and material, and a bunch of other things. Accordingly, I found that it is best to experiment with your space before electrical rough-in by mocking up the fixtures and trying them out in the location to make sure you're happy with the result. For the experiments to be meaningful, you really need to have multiple fixtures so that you can evaluate how their lighting adds in the room. During renovations, I usually just screw a bunch of fixtures on cords to the original walls and ceiling drywall and see what happens. If you're trying to preserve your finishes, you'll need to get more creative -- I've used tripods and photography light stands before too.