The laws written in Leviticus were written with the intent of keeping a small, nomadic tribe (the Israelites) alive in a hostile territory with little to no food preservation methods, no understanding of germs and parasites, and very few resources. Many of them can be explained by modern science, but the need for them isn't as crucial in an over-populated, technologically advanced culture that is not in danger of being overrun by its neighbors any time soon.
The laws for keeping kosher, in particular, have been shown to prevent cross-contamination and minimize exposure to certain harmful organisms (very specifically, Trichinosis, Salmonella, and something common in undercooked shellfish), although they do so with a broad brush of 'unclean', rather than 'safe if properly handled'. Many of the 'leprosy' laws have to do with either other infectious diseases (not Hansen's disease at all), or hazardous molds (in the case of 'leprosy of fabric and buildings').
The bits about new patches on old wineskins and mixing fabric types has to do with the fact that the natural fibers have different shrinkage rates - a garment or container of 'mixed type' would distort or even rupture, causing waste of both the material used to make it, and whatever it was containing. Modern blends involve synthetics that are spun together at the individual fiber level, which couldn't be accomplished with the existing tech, not to mention the fact that polyester, rayon and nylon are long, continuous fibers, instead of the myriad short fibers you get with wools and cotton.
The laws of sexual conduct are to maximize the survival of the tribe: Lots of children, genetic diversity (including a weird thing about a childless widow going to her deceased spouse's brother - it keeps the Y-chromosome in the mix, but it's still freaky by today's standards), and actively avoiding things that won't 'produce issue'. At the time, they didn't seem to recognize that women contribute to the makeup of the child, so lesbianism isn't really touched on, interestingly enough. The 'sin of Onan' wasn't masturbation, but 'pulling out early', which jeopardized the continuation of his brother's family (one of those childless widow things).
The bits about curses, 'witches' (the actual Hebrew translates as 'brewer of potions', aka, a poisoner), and the like are more of the BCE* equivalent of 'no flame wars, kthnx!' - if you've got people in a small group throwing curses and poisons at each other (considering that people believed in curses at the time), then the small group is going to fragment, and be more vulnerable to the environment. A good portion of the Ten Commandments (okay, that's Deuteronomy) can be summed up with 'be nice to each other'.
It's been a while since I've sat down with Leviticus in-depth - these are the ones I can remember off the top of my head.
*BCE = Before Common Era - used by archaeologists and historians in place of the religiously slanted 'Before Christ'.