I hope the trim is finished w/Polyurethane. If not, you'll have to be even MORE careful.
For the paint 'spots', you can try LIGHTLY scraping w/a piece of plastic. I've usually cut a lid, or something, from a container in my Recycle Bin. The plastic should be a little 'flimsy', like that of a plastic gallon milk jug. If this idea doesn't work, I've used a Utility Knife or an Exacto Knife to LIGHLTY scrape off the spots.
As for paint smudges, I don't know what you can do w/o possibly doing 'damage' to the wood (and/or stain), or to the poly coating. You can try the above ideas but I have no guarantee. You can visit PeelAway.com or CitriStrip.com and poke around. AT worst, you can write or call them. Just let them know if you have poly or not on your wood. I'm ASSUMING you're trying to remove a water-based paint (Latex-based paint.)