transmissible diseases are usually present in most systems, crocodiles have salmonellae naturally occurring in their intestine and amongst other bacteria they are generally unable to affect an individual until the host becomes stressed which can be the precipitating factor to septicemia. Crocodiles are affected by internal parasites, bacteria and fungal diseases and the most basic method of observing any health issue is by the animals activity level, appetite and some conditions can be seen visually as lesions or discoloration. fecal smears on a slide may be able to identify some intestinal parasites, if you take a sample to a university biology department they may be able to include it as a sample for graduate education otherwise veterinary consultation would be required.
I have experienced chronic stress dermatitis in two crocodiles one was fatal the other has received treatment for nearly two and a half years and is making a very slow unsteady recovery. Crocodiles are generally quite adept at protecting against disease (I have seen crocodiles kept in filth that were still relatively healthy) once a illness is present and noticeable it is generally an uphill battle at best.