I would like to put my grey water from my washing machine into a hole with rock in it about 75' from the house. Does this sound like a good idea? Will the soap cause a lot of problems for the ground? Is there a specific kind of soap to use, if you have a septic system?

Well, there is a huge difference between creating a french drain, which is what you are suggesting, and a "septic system".

Also, pumped water is rarely if ever considered "gray water."

Honestly, my grandma does the same thing and beilive it or not within 2 weeks doing it, she actually had grass grow more! It doesn't really seem to have a problem and actually makes your yard smell good so, I see nothing wrong with it.

To know for sure you need to check with the State officials is you live outside a city and if you live in a city check with the city officials.

Letmetellu's correct. Check local codes. In my area it's unlawful to discharge gray water into a open ditch, dry well or a french drain. Regards, Tom