My understanding of it is that a homozygous spider, while physically identical to any "het" spider, will produce only spiders when bred to a normal, whereas a het spider will produce only 50% spiders. Of course, the only way to tell whether or not your spider is het or homozygous would be through breeding. Would be a very useful breeder if it was homozygous though!
Someone can correct me if I'm wrong, but I'm pretty sure that's how it works.
EDIT: Also, homozygous doesn't mean simply that the trait is visible, but rather that both allels are the mutated gene, rather than only one (heterozygous). Heterozygous animals with a co-dominant gene do display a physical trait (i.e. Pastel is the het of the homozygous Super Pastel) but dominant genes display even in the het animal, and the "Super" form is an animal which will always produce animals with the mutated trait when bred to a normal. Hope that helps.