Every time I have to deal with the health care system, I feel like I'm going back in time. Doctors that can't even communicate by email. Redundant record keeping. So much lost information. So much lost data. So much waste. Every time I have a problem with my insurance, I have to call a 800 number and sort things out with a human being paid money to do what software could do.
Target issues with information flow. Paper patient records, for instance: everything should be computerized, with symptoms sorted by severity and time. The computer should highlight historical symptoms and diagnoses - perhaps a timeline of medical events. Make allergies and existing conditions extremely obvious; avoid having to ask patients about the past. If possible identify possibly illnesses based on symptoms, though that would almost certainly have very high rates false positive and false negatives.
Hell, you could even go so far as integrating a patient-side application for logging health state: a simple webapp where a patient can go in and report symptoms or general feeling each day. That would make it easier to identify the beginning of symptoms, as well as other illnesses. You should never have to ask the patient how they're feeling at a check-up, because they're likely to forget a lot of things since their last check-up.
Disclaimer: I'm tired, this is just stuff off the top of my head, I'm not involved with health care and have no idea whether these ideas would be useful to doctors and nurses.