The eyes should be clear and bright, with no sign of cloudiness or discharge. An eye that suddenly goes cloudy may mean that the guinea pig has got an ulcer as a result of a piece of hay in its eye. Any eye problems require urgent veterinary attention. Guinea pigs do normally secrete a milky discharge from their eyes, which precedes grooming, as they use it on their paws to groom themselves, if you see this you do not need to worry about it.
The nose should be clean, and as with the eyes, shouldn't be runny. Any discharge or sneezing may suggest that your guinea pig has a cold.
The fur should be dense and clean. Any patches of hair loss or areas where the skin is red and sore may suggest that your guinea pig has mites. Watch him closely, is he scratching more than usual? Mites burrow under the skin and cause a distressing condition called mange, and the sooner you spot any problem, the sooner you can get it treated, something your guinea pig will certainly thank you for. Sometimes you may see little tiny nits walking on your guinea pigs fur, these are hay mites, which are harmless and a simple shampoo will get rid of them for you.
Check the nails, and never let them get too long. Guinea pigs have no fur on the bottom of their feet, so check the bottom of their feet regularly for any sign of soreness. If their feet are sore their bedding wants to be as soft as possible, wood shavings and soft meadow hay is best.
Yes, this bit needs checking too... The whole area should be clean and dry. If the guinea pig is wet and smelly between its legs it may have a urine infection. Old boys may also get a problem where their poo gets stuck, and they are no longer able to eat the sticky caecotrophs as they should. Your vet will be able to show you how to help them.