One reason bulbs can burn out quickly is if the voltage applied to them is higher than the expected voltage (120V in The USA). Wiring problems and bad transformers can cause the voltage to be out of spec. Another reason is if there is a loose connection somewhere, and the light flickers (causing unnecessary heating/cooling cycles). A third reason is if the light is in a confined space, and overheats.
In order to check the line voltage, you will need to use a voltmeter. The Kill-A-Watt is a very safe product to use to check the line voltage. Note that you should try a few different outlets, since there are generally two different phases of power (not really phases, but opposite polarities, 180 degrees apart) going into a typical house, and you need to check both of them.
Identifying a bad connection is trickier. Generally, you would see flickering lights, but to be sure you would want to use an oscilloscope or spectrum analyzer (expensive equipment). Sometimes a bad switch will cause a short flicker when the light is turned on. Replacing the light switches with new high quality switches could help.
Finally, have you noticed that the bulbs go out more quickly in certain places? Are those places more confined, causing the bulbs to heat up more? If so, you need to use lower wattage lights (such as CFL, halogen, or less bright incandescents) so that the bulb is less hot.
LED lights, halogens, and CFLs are all more efficient than incandescent lights. For the same amount of light output, they use less electricity, and generate less waste heat (keeping them cooler). In order to check if they meet your needs, compare the light output (in lumens) to that of the bulbs you are currently using. Don't go by the "equivalent" rating (such as 60W equivalent).... The amount of heat generated is nearly proportional to the wattage of the bulb (generally between 10 and 25 W). Another thing to look at is the color temperature, as measured in Kelvins. More orange lights will be around 2700 K, while more blue (daylight) bulbs will be around 5000 K.
PS: Advertised bulb lifetimes are usually assuming use of perhaps four hours per day. So, a seven year bulb may only last a bit over a year if it is left turned on continuously.
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:
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.
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.
Best Answer
Depends on what you mean by "safe". I wouldn't entirely trust it with a kid in the house, but it's probably fine for adults.
On the other hand, you can make it a bit safer by screwing in a dead bulb (which, like everyone, you'll acquire over time), or one of the edison-base-to-outlet adapters available at hardware stores. I'd consider either of those approaches reasonably child-resistant, especially given that the fixture is presumably out of reach of kids anyway. Not worth the effort, I expect, but you did ask.