I've been using the same tank for about eight years and had never to use anything but water to clean. The spiral, which had to be thrown away because it was broken, had that usual brown stain but this was never a big issue to me.
I wouldn't use dishwasher because of the soap residue that might leave, it can be hard to get rid off afterwards. If I ever had to clean I'd soak in a solution with water and vinegar for a couple of hours and use a brush to clean the excess, rinse well with clean water and let it dry.