We are often asked about cleaning a glass dome. Since the glass domes are very fragile, cleaning must be done carefully. First off never hold the glass dome by the bottom. This is the weakest part of the dome.
Start the cleaning by using Windex or similar product, cleaning both the inside and outside. Wipe with paper towels until dry. If this does not completely remove any film on the glass try using a stove top cleaner with a little BonAmi (grocery store). Do not use Comet cleanser as it will scratch the glass.
Some domes are plastic and require a plastic dome cleaner so would not recommend Windex or similar products for these.