Although there are many warnings about hermit crabs causing illnesses, they do not. Unlike many other reptiles, hermit crabs do not carry Salmonella, or other harmful illnesses. They are said to be completely hypoallergenic.
Illnesses from humans: although I am not sure exactly what illnesses and bacteria can be transfered from human to hermit crab o make them sick. I do know there are some, so you should ALWAYS wash your hands before handling your crabs. This is the safest thing to do.
Post Purchase Syndrome is one of the most common illnesses for crabs. Crabs coming from horrible conditions often have issues adapting to a habitat where the conditions are ideal for them. They become inactive, do not eat, or drink, and can die from PPS. The only thing you can do for your crabs is provide them with the proper nutrients and hope they get better. Crabs usually aren't in the clear until they've had their first molt with you. The wait can be anywhere from 2 weeks to 3 months! Don't give up on your crabs!
There are many bugs and parasites that LOVE hermit crab's habitats. The crabitat is a place where many insects thrive. On some rare occasions, people have invaders in their crabitat. On occasions such as this, the best thing to do is remove all of your hermit crabs, bathe them in salt water, and put them in a clean ISO. Then boil everything you can in salt water, and replace the substrate. Most of the insects are not harmful to your hermit crabs, but they should not be ignored.