Are you using an acrylic latex, or latex based paint?
If so, be very careful about applying tape as your edge. Latex paint dries fast, but does not reach full 'cure' (depending on temperature) until many days after you've painted it. Full adhesion is reached only when the paint has cured, not when it has dried. If you try to pull a painter's tape edge on latex, you can very easily tear the paint. Don't ask me how I know this.
If you don't think you have a steady enough hand to apply the paint with a brush, and feel you must use the tape, consider peeling the tape away immediately after you've painted an area.
The other option is to run as neat of an edge as you can, let it dry for about two weeks, and then clean your glass edges up with a razor blade.
I've got about 200 individual pieces of glass left to remove, reglaze, so I feel your pain.