Know the PT requirement. Make sure you can surpass it. If your asthma does not kick in after a 5 mile run, then you are probably OK. Still, make sure and mention it at the MEPS. Your recruiter may tell you to hide it. Don't. Your recruiter only cares about his quota, not your ass. It's your ass, and you don't really know what you are getting into yet. I think Igloodude has it right there. If you are still using inhalers or have needed them in X number of years, then you won't get the waiver.
If you are allergic to penicillin, morphine, demerol, or any other drug, DO NOT LIE! Doing so could be fatal. Of you are allergic to peanut oil, same thing. Other allergies, such as to cat hair or dander will not disqualify you, but again, be honest. Nobody is going to feed you dander or inject you with cat hair.
As far as being disqualifiers for a draft, if (when) the draft is reinstated, the disqualifiers will no doubt be revamped. If they have to take one legged 56 year old men with heart conditions, they will draft them.