I live in a 130 year old 30' x 30' farm house with rock wool blown-in insulation in the rough-cut 2x5" walls, and 14" ceiling insulation located in east central Ohio. It is not very tight.
In December 2011 I installed a Fujitsu 9-RLS ductless mini-split, their most efficient model at the time (rated at 26 SEER and 12 HSPF), replacing an inefficient hot water heating system. The 9-RLS is rated to operate from 3,000 to 22,000 BTU.
I would install a second unit, but I plan to super insulate the house and am confident that this extremely efficient unit will then easily maintain a comfortable temperature.
I assumed I would need to install a low wattage circulation fan to move air around the house, but quickly decided it wasn't necessary for me. With doors open most of the time the temperature ranges from 3 to 5 degrees colder in the opposite corner of the house from the HP, occasionally more in the most severe weather.
The coldest weather since installation have been 3 consecutive days with nights at -3, +8 and -1 degrees F and day temp at 16, 20 and 19. The 9RLS was not quite able to keep up, letting the room in which it is installed drop to 54 degrees on the coldest nights. The electrical consumption for the heat pump (I have it separately metered) for those days averaged 17 Kwh per day.
I am sorry to hear some have had problems, however I have friends who together have installed a dozen Fujitsu and Mitsubishi mini-split ductless heat pumps. To my knowledge they all love them. I am aware of only one case where minor repairs were needed. It is critical that the installation be done by a competent and properly trained installer.
For efficiency, the last I checked, Fujitsu and Mitsubishi were at the top of the pack, both make several lines. I and my friends have all chosen units from their most efficient series.
It is true that the thermostat on the unit is not as effective at maintaining exact room temperature as a remote thermostat would be, especially when bringing the room up from a set back temperature, but when the unit is left on I find the temperature stabilizes close to the set temperature very well.