Clean up the digitizer with lint free wipes or a clean microfiber towel. I used some lens cleaner on a microfiber cloth to clean mine up.

I probably did a terrible job of removing the glass and the digitizer appears scratched. If yours does look like this as well it's no problem, when the screen is turned on it's not noticeable.

If you want to really get the screen almost perfectly clean or if the glue residue won't come off, use some acetone-free nail polish remover. It takes only a few seconds to get all the dirt off and it will evaporate: it will look nearly flawless when you are done.