110405-2240 EDT
dcooper:
You need to study the characteristic of various loads and their sensitivity to voltage variations. Do enough searching on the Internet and you will find substantial information.
Tungsten incandescent filament light bulbs have a lamp life that is very dependent upon applied voltage.
From
http://www.gelighting.com/na/business_lighting/faqs/incandescent.htm
3. My incandescent bulbs have been failing earlier than the specified life. Why is this?
Incandescent lamp life can be shortened by vibration or shock and supply voltage swings. If a lightbulb is going to be in an environment where it is exposed to vibration or shock, such as a garage door opener light or ceiling fan, you should try to use a lamp with a stronger filament. GE manufactures lamps specifically for these two applications along with the Survivor vibration-resistant and "Ruff-n-Tuff" rough service lamp.
Another cause of general incandescent lamp failure (other than leaving them on all the time) is high voltage. While utilities usually do a pretty good job of voltage regulation, they sometimes have little control. State regulatory boards allow them certain specified leeway because of anticipated load, local load peaks, and other criteria. The allowable limits are usually in the order of ten percent, which on your nominal house voltage of 120 volts would allow a range from 108 to 132.
Incandescent lamps are very sensitive to voltage. A lamp rated at 120 volts, for example, would only last 1/2 of rated life if subjected to 125 volts, or 1/3 of rating if the average voltage applied were 130 volts.
The first thing you should do is to keep track of how long the worst offenders are lasting. How long are your lamps burning? Be sure not to count the time that they are turned off. Typical incandescent bulbs are rated at 750-1000 hours, meaning approximately 2-1/2 changes per year.
The next step may not be easy. The only way to tell what average voltage your bulbs are experiencing is to attach a recording voltmeter to the circuit you are testing so that it records only when your lights are on. This step should only be accomplished by a licensed electrician. If you determine that you are receiving higher than rated voltage you will need to contact your electric utility to fix it.
With lower than rated lamp voltage the lamp life increases.
The voltage you have read of 124.5 V will not remain at that level over long periods. The amount of variation is dependent upon many factors. iwire gave you a useful reference table.
Since other things are failing as well in a short time, and unless the bulbs are subjected to shock. I think you have abnormal voltage conditions at times because the bulb life at your measured voltage is too short.
I would suspect a neutral problem that is intermittent, although there are other possibilities.
At my home I do not have and never have had a neutral problem. Some old photos of plots showing my home voltage for a short time shows some slightly abnormal voltage variations, the periodic repetitive nature is the abnormal factor. The magnitude is quite small. In many typical applications you will encounter the short time variation will be much greater. Longer time analysis of my voltage shows greater variation, but not usually rapid. See photos P22-P25. The red curve is voltage.
http://beta-a2.com/EE-photos.html
At the shop a few years back we had a neutral and hot problem at the pole transformers. The system has two transformers Y connected on the primary and open delta on the secondary with a wild leg.
For several years we had very short disturbances with maybe some light flicker and CNC machines shuting down. The occurrences might be months apart. Then things became more often but still seldom and quite random. Then occurrences would occur where lights would flicker, or dim, or brighten. On at least one occasion a floor fan sped up. We got voltage perturbation responses from computer UPSs. Complaints to DTE, the power company, finally got them to install a temporary line monitor. This was on-line for over a month and detected nothing even though we had disturbances. I also set up a simple recorder and saw greater then 135 V on the phase I monitored.
Then late one day things were getting much worse. Called DTE. They sent out a truck, but he wasn't the correct person. Dusk was developing. As this driver waited for the other truck he observed arcing at the transformer terminals. The neutral and one hot were both arcing. I fully believe these were aluminum wires. The transformers were replaced and no problems since then other than substation or further up problems.
With the TED power monitor I have at home it monitors the voltage of one phase and the sum of the power of both phases. It monitors voltage to an 0.1 V level. If connected to a laptop with TED's software then you can collect data over a very long time by saving the collected data once per day. The laptop should be on a UPS.
.