Last weekend, I masked the edges of my bedroom walls with green
painter's tape, painted the ceiling, and took down the tape after the
paint was dry. So far so good. Yesterday I masked the edges of the
ceiling and painted the walls a different color from the ceiling.

This morning I took down the tape. As expected, there are places where
the second taping went slightly beyond the edges of the ceiling paint,
so I have some gaps to fill in. What's the best way to do that?

Also, along just one wall, the tape brought a couple of narrow strips of
ceiling paint down along with it. How can I best fill those channels? I
guess in both cases an important concern is filling the gaps to the same
depth as the finished surfaces. Or higher--I guess sanding afterwards is
an option.

Any tips for the future on preventing these problems? I'm going to be
tackling the trim next so I'm wondering how I can avoid these glitches.