This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
There are so many ways to get into trouble with drawing that it's difficult to know where to start with what you've presented. Some comments: Looks like you are using custom Point and Line classes. I wonder what's going on in the Line class: could you be changing the line locations with each of the p1.setX(p1.getX() +...–type calls?
I experimented a bit with the getComponentGraphics method and it seems to alter the graphics context, at least the color, during the drawing of the lines. Maybe you are trying to draw only the parts of the lines that need re-drawing. Swing will do this for you automatically (double–buffering).
The scrollPane will automatically repaint the graphics located within its view extent. Here's an idea: