No specific parameters. I assume the instructors have discretion to refuse students, if they think the student has weight or fitness issues that would make having them in the class unsafe. One DOES have to submit a thorough health history to GUE, and get clearance for any prescription medications, but I think that's more a liability/insurance issue than a health concern.
Oh, and to answer mania's question, I think smoking is a bigger issue than having a beer after a dive. Alcohol DOES dehydrate to a degree, and more is worse. But especially if you are aware of it and have taken in plenty of fluid during the day, and don't overindulge in alcohol, the effect of a beer on your risk of DCS several hours after a dive is probably negligible. Nobody's ever going to get a study done to prove it, though, because the incidence of DCS is too low, and you'd have to have a big cohort of divers doing similar dives, and monitor them for a long time, to show any difference.
On the other hand, the long-term effects of smoking on the pulmonary and cardiovascular systems are well known. Moderate alcohol consumption, on the other hand, is either neutral or beneficial to the cardiovascular system over the long term.