According to Petplace.com, there are three cat symptoms that you should never ignore...here they are along with their reasoning.
1. Red Eye . A "red eye" is a non-specific sign of inflammation or infection. It may be seen with several different diseases including those involving different parts of the eye including the external eyelids, third eyelid, conjunctiva, cornea, and sclera. It may also occur with inflammation of the structures inside the eye, with glaucoma (high pressure within the eye) or with certain diseases of the orbit (eye socket). Either one or both eyes can become red, depending upon the cause of the problem. Some of the possible causes can be serious and ultimately cause blindness.
2. Coughing . Coughing is a relatively uncommon problem in cats. Coughing is a common protective reflex that clears secretions or foreign matter from the throat, voice box, and/or airways, and protects the lungs against aspiration. It affects the respiratory system by hindering the ability to breathe properly. Common causes include obstruction in the windpipe, bronchitis, pneumonia, heartworm disease, lung tumors, and heart failure. Some of the causes are life threatening and all cats with a cough should be evaluated by a veterinarian
3. Bloody Diarrhea . Blood in the feces can either appear as "melena" which makes the stools appear black and tarry is the presence suggests digested blood in the feces. Melena is different from fresh blood in the stool (hematochezia). Bleeding into the colon or rectum appears as fresh blood in the stool. Bloody diarrhea should be evaluated by your veterinarian as soon as possible.