My puzzle count:
Well,
520+135+6. There are 667 in total, right? I have no idea where to find the remaining 12. One is in the ship. Another one might guard the final cinema code (#4), but I kinda feel like it's the one in the ship. But the other 11? No idea.
I consider this the hardest puzzle in the game. Being very careful about how much I give away.
What did you have to do before when there was a second invisible line, and two colors?
Well,
each line has to cover one set of colors. In this case, one of the lines presumably has to cover two sets of colors. Though maybe this is a red herring and one of the colors actually has to be ignored? Hm. That would be a first.