FHA does not require outstanding collection accounts to be paid off (I just was approved through automated underwriting, and both me and the wife have collection accounts on our reports). The exceptions are any federal delinquencies (tax liens, delinquent federal student loans) and judgements, which must be satisfied.
Some of the lenders who provide the financing for the FHA loans will have stricter guidelines than the FHA mandates - many (but not all) will require non-medical collections to be paid off (mine didn't). From what I've heard, few, if any, lenders will require medical collections to be paid.
The age of the accounts is important though - they don't want to see any collections within the past two years, and no lates in the past year IIRC. Don't know whether they'd have a problem with recent medical collections.