I suspect that the stud which is leaking is not fitted into a blind hole i.e. the thread goes right through to the water jacket.
I would suggest that you drain the coolant - take the stud out and clean both the male and female threads and re-fit the stud with Loctite lock and seal or similar.
The other two stud holes are normally blind i.e. they do not go right through to the water jacket.
To check if the hole is blind or not put a small drill down the hole and see if it goes through into the water jacket - do not accidently drop the drill into the water jacket.
If you do decide to remove the thermostat housing refit using a non cork gasket well greased.
http://www.ebay.co.uk/itm/CLASSIC-MINI- ... SwAL9UgGYX
or
http://www.ebay.co.uk/itm/Classic-Mini- ... 1750460431
Whilst original fitment - the cork gasket is inferior to the paper / Flexoid (trade name) gasket as regards sealing also the cork gasket is prone to deforming when the thermostat housing nuts are tightened.
I note that you do not appear to have fitted the spring washers (Pt No: GHF332 (MOSS)) under the nuts. They should be fitted.