How do you tell how dirty your power is?

Plug in several ordinary low wattage light bulbs in as many sockets as are in the circuit you use for audio.add a few cheap multi A/C adapters and insert more low wattage ordinary light bulbs. (the light bulbs tend to dampen and eliminate A/C spikes, High frequency junk.
Now if your system sounds BETTER with all these light bulbs IN.... you need power conditioning. If it doesn't change... you probably do not. If it sounds WORSE.. you need a rewiring of your A/C mains
This is a VERY cheap test. You can plug in ordinary lamos etc, as long as they are common light bulbs.. (NOT Halogen, not compact flourescent)

Would power impurities show up on an oscilloscope? Can one be rented? Are you familiar with reading and operation of the test gear?

A scope is the only way to assess the non-60 Hz information on your ac. I doubt if anyone rents them, however. Don't be too certain that ac filtering, etc. while getting rid of some of the noise will sound better. Most such devices hurt the sound more than they help it.

TBG makes a good point. There are several types of power filtering, from transformers to chokes to capacitors to active re-generating devices. Each has its place and results in different trade-off's. Some can work together and others can't. Some work better for source components but not for amps. There's more to this science (yes, science, because each has a provable result on dirty power sources) than just buying something and saying "it helps" or "it makes things worse".

There's a lot posted about power conditioning on many forums. Do some searching and read up a bit. Then by all means, buy something used that makes sense and try it out. But just because that may not work doesn't mean that the correct type of power conditioning isn't needed in your room.

Enjoy,
Bob