First, I addicted my wife to my new game, even in the rough state it was last week. This alone shows that a game has promise, since my wife would be exactly in my target demographic.
Second, a number of visual improvements. The connector sections are slightly narrower than the nodes (to make them easier to pick out). Color choices have changed slightly.
Third, the Reset, Undo, and New Game buttons. As it turns out the long load time has nothing to do with generating the maze (as you will be able to see if you click on New Game... for me it is nearly instantaneous). I think the problem lies with the creation of the IMG objects, which is done (foolishly) by appending text to my DIV's innerHTML property.
Fourth, since a puzzle never loops back on itself, the game will not allow connections that cause a loop to form.
On the "TODO" list:
1. Different sized boards (4x4-16x16).
2. A better "a winner is you" than an alert.
3. A Timer, starting only after the first move is made.
4. Game number/random seed.
5. Improve graphics, especially buttons.
6. A "Solve" button.
7. Repackage as Yahoo! Widget. (The original intended platform)
8. Repackage as Google Gadget.
9. Help file, including tips and trick for solving a puzzle.
10. A tool that allows one chain of connected nodes to be completely disconnected.
One thing I'd like is a way to mark or lock the if I know they're right. There are times when I have to go into the realm of speculation about a link, and if I could mark everything that I know is right, it'd be easier for me to undo the speculative stuff.
Also you should make an AIR version. No particular reason except that it'd be interesting. You can make standalone javascript apps with AIR, so get to work on it.