Question: I put that painters tape on the edges by the ceiling and cut in next to it (overlapping the tape with the paint somewhat).

A couple of hours later, I pull the tape, and small sections of paint come off with it. How do I avoid this?

Is it sufficient to just take a small brush afterward and touch up the area? It always seems to look crappier.

Answer: 
Remove the masking tape immediately after painting so that there's no time for the skin to form over the join between the tape and the painted surface.

If the paint has already dried, use a craft knife and a straight edge or ruler to cut it along the edge of the tape.
I find that using a hairdryer to warm the tape helps it to peel away with very little force and no damage