Welcome to the Grumble, Linda.
You must keep your work area as clean as possible when cleaning glass and I recommend handling all glass with glass handling gloves when removing it from the carton or cutting it. You will save yourself alot of cleaning and inspecting if you keep all body oils and finger smudges to a minimum.
I use LJ's glass cleaner and plain old cotton diapers or, lately, white cotton terrycloth wash cloths. I don't worry about anything shedding off of these cotton items as my cleaning procedure will get all those specks in due time with very little misses. It just works well for me. I have been doing this for about 10 or more years and would have changed my procedure if it wasn't working better than anything else I tried. I am my own worst critic, from what others tell me. So, if it doesn't work, I change it until it DOES work.
I clean glass on a board that I built out of a couple of sheets of double thickness shipping cardboard and some black kraft paper. It works very well with the black kraft paper showing up all the little specks and also smudges and fingermarks (if you don't wear glass handling gloves).
I glued the cardboard sheets together and simply ATG the black kraft onto the boards as shown below.
Just fold over the kraft paper to the back of the boards and ATG the edges down. When the paper becomes dirty or torn, you can pull it off the boards and replace it with clean kraft. when I'm not using it, I slip it into one of the slots under the work table that holds my matboards. (See top photo)
Regarding cleaning the images and the mats, it is my technique to always keep the image, mats, and glass vertical from the time it is cleaned until the cleaned image, mats, and glass go together. Here is what I do:
1. I use an anti-static brush sold by many framing suppliers and I first brush the image to remove all visible dust. Then I stand the image up against my roll of dustcover paper on the end of my bench.
2. I brush down the mats both front and back and stand them up against the image.
3. Lastly, I clean and brush the glass in a vertical position and I hold it there with one hand as I reach over and move the mats and image up against the glass.
After each part of the frame package is cleaned and brushed, I never lay it down until the glass is on the front of the package, then I lay the entire package down on the glass cleaning board and lay the frame over it. This seems to keep any airborne dust from floating down and landing on any of the package parts. It becomes sort of a routine once you follow the general steps and put together your own method of assembling the frame package.
Very few times do I have to take the package apart to remove something and, usually, that is because I got in a hurry and missed a little dust nib or speck. Sometimes you will have the frame "shed" something as you place it over the frame package but that just has to be dealt with as it happens. No amount of careful cleaning will stop a little wood sliver or other kind of "critter" from sneaking in under the glass occasionally.
One other thing, when you start to shoot the framer's points in, place a point at each of the four corners of the frame and then lift up the package and do a final look-see to make sure you haven't missed anything. It is a real bummer when you sink in about 20 framer's points and THEN notice that there is something sitting there on that pretty black mat that wasn't part of the original plan!
Hope this helps.
Framerguy