The most important things to watch out for when caring for a pet rabbit are the eyes, their droppings, and their attitude. Strange as these three things may seem, they can give you vital hints as to the health of your pet.
The eyes can show the state of a rabbits' internal health, so it is important for them to be clear, bright, and healthy looking. Rabbits whose eyes are cloudy or are always watering can have a gastrointestinal problem that needs to be addressed. Unfortunately, the only way to properly diagnose this is to have your bunny see a veterinarian.
Other possible problems could be as simple an un-alarming as the bunny having scratched its eyes on something around the house or having a reaction to something around the house (dust, hair, etc). However, since the problem can also be of a very serious nature, it is best to have your pet looked at just in case. You should make sure to inform the veterinarian of when the problem started, whether the bunny has been pawing or scratching at his eyes, any dietary changes, and of any environmental changes that have occurred in the last month or so.
A rabbit's droppings are very similar in that they also show the state of internal health. A rabbit's droppings should be compact, yet able to break apart easily when handled. Droppings that are too dry, hard, loose, or wet, signify a problem. These should be watched carefully and if the problem persists tell your veterinarian. Possible solutions you can look into would be to change the rabbit's diet. Allow them to eat as much Timothy Hay as they'd like, but not too many treats (such as dried fruits, rabbit crackers or cookies, etc). Too many of the aforementioned can give the rabbit unnatural stool and cause health issues.
Lastly, your rabbit's attitude should always remain very curious. He should seem playful and be very active. This is a fantastic way to tell if your rabbit is feeling well or not. An unhealthy rabbit will be very lethargic. They won't want to play, run around, jump, be pet, etc, they just won't seem to care. This is a sign of illness and should be looked into. Just be careful not to mistake a sleepy bunny that has had a full day for a sick one, or one hiding from the summer heat for a sick one. It is okay for your rabbit to lay around a bit, but they should also be playful and extremely curious in turn.
Watch these things carefully, play with your bunny, and spoil them rotten! You're sure to have the best and happiest little pet there ever was!