Load up your rag or sponge from your cleaning-solution bucket, and scrub. Before redipping, rinse the sponge in a second bucket filled with clean water. Caulk all cracks Filling gaps with a paintable acrylic-latex caulk cuts down on drafts and makes your trim look better than new. Also, instead of using a nail to break the inner seal, use a small wire so you don't stretch out the nozzle. Also consider buying a dripless caulk gun, which will automatically back off the pressure after each pull on the trigger to prevent unwanted oozing.
Paint can bleed behind the tape, or remove the paint it's stuck to.
Another problem is bridging. Removing painted tape can tear the skin, resulting in a ragged rather than a sharp line. Lastly, taping takes time. To prevent bleeding, Span uses a putty knife to bed the tape. After letting the paint dry, he scores the edge of the tape line with a utility knife to avoid tearing the paint.