The nails must be acting as a good thermal conductor and, being in closer contact to the outside wall at the pointy end, are reducing the surface temperature of the wall in the immediate vicinity of the plaster, under the nail head. The reduced surface temperature means that natural water vapour in the house is more likely to condense on the cooler surface.
The ways to stop it are:
1) Increase the temperature of the room a bit
2) Reduce the amount of water vapour getting into the room - have you tried to see what happens if you keep the door closed? You're not using the room for clothes-drying perchance?
3) Circulate the air in the room a bit more with a small fan.