I hate saying it, and I've seen it. When there's many many many more applicants for a the available spots, what pretty much always happens is there's too many applicants who are too similar, so the admissions board starts tossing people out based on arbitrary and often unimportant sounding data because they have nothing else to go on. E.g. the way a sentence was worded "I like that guy's opening sentence better." Don't believe me? I've seen it. There was a special on NPR last week where they talked about it and the admissions boards for several schools said they all encountered the same problem. Data from industrial/Consult-Liason psychology studies show that the usual methods (grades, LOR, personal statement) leave so much information unanswered.
Unfortunately, the best indicator of a future good student was the person's performance on a standardized exam designed for the particular field of study, but as we all know, that too is a very poor indicator. I'm sure we'd all agree that one should not be defined solely on their SAT or MCAT examination score.
Someone with a prior crime is certanly something an admissions board would not find arbitrary or unimportant, especially given that there are often hundreds of candidates for 1 spot for medical school with squeeky clean records. In such a case the person would likely not even make it to the "let's toss this guy out based on the arbitrary" level.
The person could not mention his criminal past, but if anything showed up that he was not accurate in his application, this could haunt the person later. I don't know how much medical schools are keeping tabs on this since times have changes and things have become more computerized. I also cannot recommend a person lie on an application. It's illegal.
The best thing for a person in this situation, IMHO, is to see what they can do to get the charge expunged or the charges dropped.
As a friend, I'd tell him to worry about getting off the drugs first. If he can't even do that....
to look for another degree,such veterinary school
From what I understand, its even harder to get into vet school.