If you car is caked in sh*t then it wont get it looking spotless. You can use a mitt but I would be very careful when using it. What I would do is get it back to a clean state by.
Good pressure wash.
Snow foam.
Pressure wash that off.
Then I would use the two bucket method clean the car very carefully rinsing the mitt after every panel.
Dry it with a towel if possible.
Just make sure you are careful and it should be fine.
Then I would just keep on top of it using a pressure washer and snow foam.
Has your car got a couple of coats of polish and wax on? It will help a lot. Mine and my old mans car where in the same state of dirtiness. I snow-foamed mine with the method in my first post, did the same to his but mine came up a lot better than his.
I am assuming this is due to the protection on mine and the lack on his.
I am not a professional detailer but I do like to keep my car clean and read up on detailing! (Go to detailers world for lots of info)