I've hooked up most of my audio & video gear to an APC SmartUPS 1500 rackmount unit.

Recently I've noticed a new problem, that may or may not have come up about the same time I re-wired some things. Specifically, I tied all electrical componets together with an 18awg wire screwed to the chassis of each component (for reducing ground hum).

The problem is that whenever I turn on or off my living room lights, or my a/c kicks on or off, I get a complete audio drop-out that lasts for a full second, maybe 1.5 seconds.

I've tested the APC by unplugging it from the wall and it switched to battery power just fine.

I thought the APC's were supposed to resolve any odd electrical issues? How can I be getting audio dropouts like this?
I don't seem to have any video problems.

First of all, I feel your pain and had the exact same problem for years. I would go through your entire house looking for bad grounded outlets, reversed wired outlets, loose connections at any junction box or outlet/switch, ANYTHING that is wired poorly or incorrectly.

I actually had voltage running across my ground of 40 or so volts and it was from an incorrect wired outlet. It was not an easy find, but if you take your time, you should be able to find something that is causing it.

Thanks for the suggestion. I hadn't considered to check my ground for voltage. I think I know how to do that and will check it when I get home from work.
The APC says everything is fine, but it may not check for this.

I agree that you probably have a wiring problem.
By far, the easiest way to start is to get one of those three prong outlet testers and go through your entire house-outlet by outlet.