What are the minimum requirements to pass the FAA medical exam?
There are no height or weight requirements as far as I know and you dont need perfect vision. I wear glasses and have a "corrective lens" note on my medical. I think that at minimum your vision needs to be correctable to 20/20. See this link for some information as well as the information for doctors here. You can also get special dispensation for certain medical conditions. 

On a small side note, if you are asking this in relation to a Private Pilot License, they may be doing away with the current third class medical regulations which will ease the regulations greatly.