Is there a layer of something on your moldings? A few things to try:
- Use a Swiffer sheet and lightly rub
- Use a dampened sponge and lightly rub then dry
If neither of these ideas remove the grime from your molding, you may have dust in your paintable caulk. If so, you can get a can of matching molding paint and paint the top of your molding. As long as the paint color matches, the fresh painting job will blend in with the entire molding and look freshly painted!