OK ladies, here is what you need to know:
First of all, I use this stuff called Pel-Tex(it may be Tim-Tex across the pond) instead of batting when I make my mug rugs. This makes them nice and firm, so making it easier to get a nice edge(but even without it I do my satin stitch the same way).
When doing my SS, I start with as setting of 2 for stitch width. I make sure the needle is hitting outside of the edge of the fabric and I start with the needle inside the fabric as close to the top edge as I can(without eating up the fabric in the feed dog). Then I stitch until I am all the way to the bottom edge ending with the needle off the fabric.
I realign the corner of the fabric with the needle on the outside of the fabric and stitch to the bottom again. I do this on all four sides. If I have threads sticking out, I trim them and start all over again with at stitch width of 2.5.
If I have good coverage(sometimes the weight of the thread does not cover as well as I would like) I end back at where I started and tuck all thread beginnings and ends in a needle and run them through to back of the satin stitching. Then, on the back side of the fabric, I use Fray Check on the corners.
Any more questions--let me know and I will try to answer. Oh, and if I don't have good enough coverage, I do it all again using a stitch width of 3.
One more thing--I think the reason I get a pretty good satin stitch is that I make sure the needle hits off the fabric when it hits on the right-hand side.