Has Anyone Placed Power Conditioner On Its Face with the Power Outlets Facing Up?

I would be careful, as the product designer probably didn’t think of that. :)

Thanks @erik_ This was my thinking also. Obviously there is more stress on the cabinet. Will that stress cause the transformer to buzz or hum? Probably one of those unknowable's isn't it?  

 Will that stress cause the transformer to buzz or hum?

No, this has to do with the laminations of the transformer itself as well as the incoming power, now how it rests. Now, if it IS already vibrating and you tweak the cabinet so it's more resonant, that's' another story.

Don’t think it matters.  Keep cords separated, and hear for electrical issues

 mess w cords, rca’s, power cords, CD player, 

I use a Furman line conditioner, and a monster me in 2nd system, monster one is poor quality, tweeter static, etc!

mess w it til u get the sound u want!
replacemcords, rca’s, from CD player, preamp, amps, etc!

 Tinkering is key

If it can survive shipping where it is violently thrown around, it will survive being gently placed on its side.