Ohhhh, big can of worms here for some people. Here's my impression.
On some pieces of equipment I definitely hear a difference with AC inversion - changing the orientation of the AC plug. The "correct" orientation results in an expanded soundstage and more space around the instruments (less flat than the wrong way). This is readily observable and easily heard.
Correct phase polarity on digital sources is less easily perceived (by me at least). Som people tell me that one CD may be phase correct, while the other is inverted. Others say that alternating tracks each have reversed phase, so if track 1 is in phase then track 2 is out of phase, and so forth. Far too much work to keep changing back and forth, or to identify and lebal each disk as a whole even.
The sonic effect of correct phase seems to be a clearer and better defined high end without compression. A subtle difference, for sure, and many audiophiles I know can't hear a difference at all. Many times I can't either, so I usually don't bother.
My recommendation is to work on the AC polarity in your system first. That seems to be readily observable and beneficial to many people who have tried it.