If you've never thought of this, use a baby bottle brush to get your drinking glasses clean. They are great at getting into the nooks and cranny's where your hands more than likely can't get.
Also, Mr. Clean Magic Eraser boxes have coupons inside of them. I use them for everything, to wash pots and pans, clean bathrooms, and even getting the stains off the bottom of my pans.
This was somewhat after I had started cleaning the bottom of it.