Something to note is that the application process changed this month. All "pre-clearance" has pretty much been moved to after invitation, including all medical tasks and paperwork.
In the present system, once you submit your application, you will receive an automatic reply requesting that you complete a Health History Form (HHF). Be totally honest on this form, as it will tell you which countries to which you are "pre-cleared" for invitation. After you submit the HHF, you'll fill out a country choice form based on your pre-approved list. If you're invited, you'll then have to undergo final medical clearance, which will be quite a bit of paperwork due to your longer history. But this is also why it's important to be totally honest on the HHF. If you don't disclose something, you could get invited to a country for which you will not receive final medical clearance (and thus you won't go and all that paperwork will have been a waste).
All I've ever heard from the Medical Office is that there is no such thing as an instantly "disqualifying" medical condition. Everyone's health is evaluated on a case-by-case basis, and assessed in comparison to what each country has available in medical resources. The new website (where you can search through the particular countries/programs that are currently accepting applications) includes information about each country's medical support services and a list of which conditions could probably not be supported in those countries (i.e. Country X requires all trainees and volunteers to receive a yellow fever vaccination, so you may not be able to serve in Country X if you have an egg allergy).