Here are a couple of tricks:
1: Use monofilament fishing line drawn tight and held close to the paint and 'floss'using a sawing motion behind the doublesided tape, closest to the paint. This is slow but takes most of the tape off when you take the trim off. Residue will still remain.
2: 3M makes an adhesive remove that works OK, not great, but OK. You can buy it at autozone, wal-mart, etc
3: Get an eraser wheel. They work on a drill and really speeds up the process. Google it if you've never seen one.
I've replaced all the trim before they invented eraser wheels, so I was stuck with plastic scrapers and adhesive remover. Never again. I'm about to paint Mighty Whitey, so I invested in a wheel. Haven't used it yet, but know people who have and they likey.