Odds are that it a wiring problem.
It's fairly common in apartments and "tract homes"
It's also simple to deal with. First thing is to find out if the house wiring is the issue. If you CAREFULLY pull out one of the outlets in the wall. Look at the 2 or 4 wires running into the back of it. If they are screwed in, then this isn't your problem. if they are simply pressed into little holes in the back, then you have found the problem.
The thing with the outlets is this; when they are pressed into the little holes, they are only making contact with a tiny surface. (about 1mm x 2mm) When they are attached by the screw posts, they are making the best contact and the power flows better.
It's not hard to attach them correctly. You just need a set of wire cutters / strippers and a screw driver. The hard part is the fact that you have to so this to EVERY OUTLET in the house.
It's not fun... I know, my house had 41 miss-wired outlets when I bought it...