To clean dial, always use blower and a sharpened piece of pegwood or toothpick to remove dust and broken pieces of glass from surface. Then use Rodico or something like it to remove any other residue. (Rodico is like silly putty and can be purchased from most material distributors.)
It is always best to remove the hands when cleaning the dial or to straighten them.
If the dial is very dirty, remove it and clean it with a soft dial brush. If that doesn’t work, use a very mild detergent and a soft brush. Be sure to dry the dial immediately. If any liquid stays on the dial for longer than a few seconds damage can and probably will result. I suggest you use extreme caution when putting any liquid on a painted dial, but I do clean many dials with a mild detergent I mix up and have excellent results. This will not remove spots but will remove dirt and yellowing. If lacquer is damaged there is not a lot that can be done but I have had some success re-lacquering dials as a last resort.
Genuine baked-on enameled dials, like old pocket watch dials, can be soaked in detergent in an ultrasonic cleaner and will clean up beautifully. Be sure not to leave the dial in too long; check it often. Usually a couple of minutes will be sufficient. Take extra care if you have a large, very powerful tank. If the dial has chips or loose pieces they will come off so be careful. If the dial is extremely delicate obviously do not put it in a powerful ultrasonic machine.