5 screws in 7.6 seconds.

I am a first-time homeowner (and never lived in a house before -- apartments my whole life). We have been living in our ~50 year old Cape Cod since January. I have been reading this site and its forums for a few months and find it to be quite enlightening and informative. Over the past few months, my wife & I have gradually noticed that a lot of the nails in the walls (as well as the pitched ceiling in our upstairs rooms) have started to pop out. I have read some articles elsewhere where they mention screwing a drywall screw into the stud about an inch or so above/below the nail as a fix. I have done this for a few places but as the weeks pass, more and more nails are becoming visible in almost all walls in the house. The upstairs rooms (pitched ceiling) in our Cape Cod are also exhibiting this behavior (which is worrying my about the ceiling falling down). I want to call someone to take a look at our house (I'm guessing a structural engineer), but I was wondering if anyone here had any opinions/guesses/suggestions. I think we may also have some moisture coming into a wall from a dormer upstairs but the nail popping is not confined to the area of the house beneath it. I'm hoping to be able to talk somewhat intelligently and understand some common issues before and when I call someone in. Thanks!