Is it possible to get a FHA loan on a condo?

Yes but it must be an approved FHA project.

A good friend of mine saw his loan application fall through for this exact reason, i.e. the lender backed off after seeing the fine print on the contract governing the apartment complex.

Amy, anyone can get a condominium project appproved. I've done that for some of my borrowers. The problem is that FHA takes 6 weeks or so for the approval after all the paperwork has been submitted. That's fine for a refinance but many sellers might not be willing to wait that long just to see if you can apply for FHA financing or not.