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: 
Mistakes are bound to happen, and yes you can touch it up with a very small crafting paintbursh (like the ones kids use for waterpainting). You will probably never notice. 

The best solution however, is to not use painters tape on corners and ceilings. Typically in professional painting, tape is not used. If you use a small 2" cutting paintbrush, and apply by pulling the paintbursh at an angle toward you, keeping the smallest amount of bristles near the corner / edge, you will be fine. The only time i apply painters tape is around trim - and this is more to prevent drippings and splatter, than to protect a clean edge.

If you get paint on the opposite wall using this tapeless method, it is most easily corrected by fixing it immediately when the pain it still wet. Simple use a all-in-one paint tool (or a putty knife) with a damp cloth (i use old t-shirts) pulled tight over the edge, then scrape away the paint that got on the opposing wall.
I find that using a hairdryer to warm the tape helps it to peel away with very little force and no damage