Some Light Reading -Army Fitness Standards
Attached is a link to Army Regulation 40-501 - Standards of Medical Fitness, which is exactly what it says. I believe it is current but can't guarantee it. It's a while since I studied it but note that some standards apply to enlisted men and others to Army ROTC.
http://www.apd.army.mil/pdffiles/r40_501.pdf
As Pima said, everyone has a story, and anecdotes are not statistically valid. However, based on Dim Son's experience, some lessons are available.
He had as I recall 3 or 4 separate DQ's, which were all eventually waived, though there was no certainty this would be the case. The ROTC being his idea, he managed or mismanaged the process himself, up to the point when he was offered a scholarship at a school to which he hadnt applied (a hazard of Early Decision - another story). Among other things he arranged for eye surgery at an inopportune time, which triggered one of the DQs. (That was about the time I became acquainted with 40-501). Because he applied in time only for the last board, which was a late one that year, the necessary waivers were not obtained until he was already at school.
So:
1) Get your application in early
2) Organize your medical records, especially if there have been issues.
3) If after the physical exams (which are done at the DoD's expense) you get a letter indicating a medical DQ, don't be discouraged since many DQs are waiverable.
4) I found the DODMERB staff helpful in explaining the process, though if your offspring is over 18, they will have to give authorization in writing for your involvement.
5) If you mail any records, keep a copy. (these days stuff gets scanned and emailed).