I also live in an apartment, which precludes me from running a true dedicated circuit from the breaker box to my audio system. What you might want to do is to figure out which outlets are on which circuits. When I did that I found that I could power my system off of it

Are the audio outputs of TV, Cable box, or the DVD player hooked up to the audio system? If so the audio cable's ground is introducing the second ground. As a diagonostic step try disconnecting the coaxial cable that carries the TV signal that goes from the wall into the cable box. If the hum goes away then we know that the hum was caused by having two grounds with different potential.

If the ground is the problem try:

http://www.xantech.com/Infrared/Infrared/IRAccessories/63400/
This one is only about $9 but it tends to knock out higher TV stations in digital cable systems and negatively affect pay-per-view and movie on demand capabilities. It's cheap enough to try and throw away if it doesn't work. But in my experience it usually causes some kind of problem. I only mention it to present all options.

http://www.klipsch.com/products/details/magic-box.aspx
It's about $100. Which is expensive by comparison but because of it's greater bandwidth tends not to knock out higher TV stations in digital cable systems. Nor does it usually cause problems with pay-per-view and on demand functions.

Tributaries used to make one but it doesn't look like it's available any more. It worked as well as the Mondial.

http://www.jensen-transformers.com/datashts
Jensen makes all kind of isolation transformers. This one looks good but, unlike the other ones I've never used it myself.

You can try this thing. First see if your outlet is even grounded...

http://www.21best.com/21_best/electronic/security/video/filters/for_sale_.html

I agree with Jim about checking the house power grounding. But 30-40 years is not so long ago, and I assume proper grounding was the law then.

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The outlets that are wired to the same circuit is confusing and strange ... I've decided I should get better power protection

If your concern is that the breaker might trip when you're listening to music, I doubt that would damage anything. It might make a pop through your speakers, but otherwise the breaker tripping is no different than you turning off your power strip.

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Can the somewhat crappy wiring cause obvious interference?

If you don't hear interference or hum etc when the system is on with no music playing, then the power line is not the source of interference.

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I definitely have humming issues ... mostly involving my TT and phono pre.

Yes, but that's not uncommon for phono preamps. If the hum happens only with the phono, then it's a grounding issue within your own "intra-system" wiring and unrelated to the house wiring.

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(1) Is it possible that the power in the apartment causes humming in the equipment?

Possible but not likely.

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(2) Would a power conditioner potentially solve the issues?

Doubtful, but you might buy one from a place that will give you a full refund if it doesn't help. If you buy local you won't even be out the two-way shipping.

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(3) Related note: Can the proximity of power cords to interconnects and quality of power cords combine to create interference?

Yes, at least for photo preamp inputs.

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If so, would higher quality power cords potentially solve this (even a decent $15-30 one)?

No.

Does the hum go away when you unplug the turntable's AC power? If so, then that confirms it's a "local" ground loop.

Also, if you can figure out the common outlets, I'd run an extension cord to the air conditioner from an outlet that is not on the same circuit as your audio gear.

--Ethan