I am currently renting a single story 1167 sq. ft. home that was built in 2004. The home uses an electric heat pump and seems to take a very long time to raise the temperature (about 2 hrs for 4 degrees - outside temp is in the 50's). Even when the thermostat says it's 74 degrees it still feels cold in the house. I own a 2 story, 2100 sq. ft. home built in 1999 that can raise the temperature 4 degrees in less than an hour (electric heat pump also). I do not want to bother the Landlords if there is a simple "check" I can do to evaluate the efficiency of the system myself first. Any ideas?

The first thing to do is to ascertain whether the thermostat is reading correctly. Hang a thermometer right next to the thermostat and let it come to equilibrium. Then put it in various other places in the house to see if the homogeneity of the temperature is what's causing you to feel cold. The results will probably suggest what is wrong and what you have to do next.

Here is an excerpt from here: Heat pump air temperature - Heating & Air Conditioning Forum - GardenWeb (http://ths.gardenweb.com/forums/load/hvac/msg1012213014548.html)

November 11, 2005
Temperature Rise between register very near heat pump plenum and return air duct 6 feet from furnace

Measured Quantities. Heat Pump operation.
Location of measuring thermometers: Thermometer in hot air register immediately next to the furnace about 2 feet from plenum. Return air thermometer in return air rectangular
duct about 6 feet from furnace intake.
Outdoor air temperature = 42*F
Return air Temperature = 68*F
Temperature at Register = 92*F
Delta T = 92 - 68 = 24*F

Calculated Quantities. Heat pump operation.
2 ton Carrier 38YXA heat pump output at 42*F outdoor temperature = 22,000 BTUh
Furnace cfm setting for heat pump operation = 865 cfm
Delta T = (BTUh)/cfm x 1.08 = (22,000)/865 x 1.08 = 23.54 *F close enough to
measured delta T of 24*F.

Conclusion: The heat pump is working within specifications.

Basiically, you will have to measure the temperature rise over the heat exchanger and correlate that with outdoor temperature and the specific BTU output for the model in question.

At 50F the backup heat should not be on.

Heat pumps are slow.