I'm guessing that Julia is studying for the City & Guilds Level 2 Certificate for Dog Grooming Assistants.
The first bit I would have thought to be self-evident. A dog which is being groomed may have a fungal skin condition (which, in a thick-coated animal, might not be immediately apparent to the groomer). Fungal spores (possibly on flakes of skin) could be transferred to the clipper blades. Unless those blades have been treated with fungicide there is a risk that the fungal skin condition could be passed on to animals which are subsequently groomed with the clippers.
I don't know the 'official' answer to the second part of the question but common sense dictates that blades would need to be sterilised if a dog's skin had been nicked by them, meaning that there was a risk of transferring blood-born diseases from one animal to another. Since a small nick to the skin might easily go unnoticed, 'good practice' would seem to dictate that the blades should always be sterilised after each use (or, at the very least, after any grooming activity when there was any risk that a dog's skin might have been broken)