To remove the black spots that get left on when you burn things, you can do one of two things, 1) take one of those tablets for using in the dishwasher, put water in the pan and let it boil for about 20 minutes with the tablet in the water. or 2) if the pan is stainless steel, use something like VIM the cream cleanser and a scrub pad.
I once burnt oil on a pot making pop corn (whoops forgot about it) and after a few times with the dishwasher tablet, the stains all came off.
If it is the bottom of the pan (i.e. the part that sits on the heat) then use VIM or CIF or whatever brand you have. If it is the part of the pan where the food is cooked, then the dishwasher tablet should work very well.
As well, that is a good way to clean the things that catch the drippings on an electric stove you know the pans that go under the elements, put them in a pot of water on the stove top with the dishwasher tablet in it. Probably using the same amount of powder that you would put in your dishwasher would be just as effective. I keep a box of the tablets. I don't have an electric dishwasher (I am the dishwasher *grin*)