Nose condition.

               If your hamster has a wet or running nose it's a sign of a cold or he has sniffed in some dust or food particles,  Oats, grain dust or even sawdust from his bedding. Find out which and rectify the situation

Teeth.

                     Check your hamster for signs of broken teeth.
Feet.
             Check the bottoms of the feet daily for signs of abrasion, infection, or sores. Sore feet can result from poor sanitation, clean your Pets cage regularly with a proprietary cleaner.  Check his housing for rough spots on the timber or wire, this can also cause sore Feet. 

Droppings.

                       . There are several warning signs that will be obvious if you check the droppings daily. Droppings that are diarrhoea-like, or contain mucous or blood, are a strong sign that your hamster needs to visit the vet. If the droppings start decreasing in size, or if your hamster stops producing droppings, veterinary attention is needed.

Hamsters can occasionally get wet tail, this looks as if  the hamster has bathed in a water pot  but it is stained yellow and will need veterinary attention immediately.
This can also be the sign of a urinary tract infection.

General  feel.
               When you pick up your hamster, you should immediately be able to tell if it "doesn't feel right".

Coat.
            Look at your pet's coat. Does it have any fleas in it? or any white dandruff-like particles, or black flea-debris? Is its skin flaky and dry? Are there any cuts, wounds, abrasions, sores, scabs, or other breaks in the skin? If your hamster has any of these problems,   you will need to treat him and take corrective action to prevent them from coming back.

Most hamsters live a normal healthy life, the conditions referred to above  are the exception rather than the rule.