Home composting is perfectly safe, especially when you follow some simple and fairly obvious rules.

Wear gloves when handling compost or working with your bin. Wash your hands afterwards.
Keep your bin covered and working correctly.
Collect kitchen waste in a covered bucket. Empty it into your bin regularly.

Occasionally problems arise but they are easily avoided by making sure your bin is
  sufficiently moist, but not soggy
  as hot as possible
  working fast
advice on how to succeed in How to Compost
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Aspergillosis
A Buckingham man died in June 2008 after spreading a mulch in his garden. He went to hospital suffering from chest pains and died 4 days later. He had inhaled a heavy dose of Aspergillus fumigatus, a fungus that is present in decaying leaves and woody vegetation. The spores spread in dry dust so can be inhaled. People can absorb tiny quantities in many situations – when mowing the lawn, potting plants, raking leaves or even walking through a wood. Only a very small number of people are sensitive to these spores, and the dose has to be very large to be harmful. The fungus can occur in the top 30-45cm of a compost heap, but will not affect the vast majority of people.
Prevent dust by keeping the contents of your compost bin moist. Avoid dry corners.
Mix plenty of green sappy material like grass mowings, annual weeds and vegetable peelings into your bin.
Pour in a bucket of water if the contents of the bin seem dry.

A wasp bike (nest)
Queen wasps may build a bike in a wooden compost bin, when the material is dry. Keep your bin moist, by watering if necessary

Ants
Ants are perfectly harmless, but will only nest in a dry compost bin. The heap can dry out at the edges, especially in slatted bins, and this is where you will find a nest.
Keep your bin damp to avoid the problem. Pour on water if it seems dry.

Fruit flies
Flies are attracted to decaying fruit skins and cores, as well as raw kitchen scraps.
Cover this material with fresh grass clippings or a thin layer of top soil to mask the smell.S

Rats and mice
If they are already in your garden, they will be attracted to your compost heap.
Prevent them from getting in by placing your bin on a layer of fine wire mesh, wrapping the mesh securely round the outer base of the bin.

Broken pots and prickly leaves
Be sure not to put pieces of broken pots into the bin by mistake. Holly leaves and rose thorns take many years to rot down.
Wear thick gloves when emptying your bin.

If you collect fruit and vegetable peelings in a bucket make sure you empty it daily. If you can’t, because your bin is on your allotment, don’t keep the collecting bucket in the same room in which you prepare food.

If you have asthma, hayfever or suffer from allergies be extra careful to keep your bins and buckets covered.

Composting is a natural process that occurs in your garden and in the countryside. It is nature's way of recycling all organic material. By composting at home you are encouraging this natural process and enriching your garden.