What could be causing cracks in the drywall of a newly renovated home?
I am not a structural engineer.  I'm just a homeowner/remodeler.  This kind of diagnosis requires a site by a structural engineer.  If you are really concerned about your house, I'd recommend hiring one for an hour or two to visit your home and provide their opinion.  Cost is likely $125-$250.  Don't get talked into making complicated drawings for lots of money unless they see that there is a problem.  You may already have some drawings if you had a permitted remodel.

However, I can talk about what might generically cause issues like this in a house.

There is, as BrownRedHawk suggestions, the benign explanation.  These crack could be normal signs of age, material expansion, or harmless settling.  If these cracks are primarily at corners or in lines at seams in the drywall, then they may simply be a bad mud job on the drywall.  Even how you hang the pieces around doors and windows can significantly affect cracking.  If it is the benign problem, you could probably just have a drywaller redo the cracking joints, possible with fiber tape if that wasn't used last time or corner beard, and see if it cracks again.  I wouldn't do that until you eliminate the more serious problems.

However, you could have more serious problems.  

Some possibilities:


if you have an especially wet year, especially in areas with clay or
a high water table, expansion of clay soils could cause some lift and
settle of the house or the water table could cause a new range of
settling.  If either problem is chronic, it should be addressed with
floating basement walls and/or basement slab drainage.  Neither are
cheap solutions.  You probably know best whether you live in a high
water table, a clay soil area, or had a very wet or very dry year.
If door and window operation is affected or if enlarged or added any windows, the structural elements around the window or door may
have been compromised or installed incorrectly.  During an old
remodel, I found two previously remodeled windows where the header
was unsupported (improperly installed).  This could cause some
movement in the wall or ceiling around the window, cracking the
drywall.
If you removed any walls during the remodel, even if you didn't think they were structural, they may have been accommodating some
other structural weakness in the house.  If you did this kind of work
and that is the area that is cracking, you'll definitely need to talk
to a structural engineer.
Did you convert any flooring from carpet to tile?  Tile, especially if properly installed on concrete board, is quite heavy.  If some
element of your structure was at its load, the tile load could have
caused some settling into the new load.  I might expect some cracking
tile in this situation.
Were any roofs lor gutters or drainage systems altered or compromised during your remodel?  Is it possible you now have
drainage water running next to your foundation etc that was
previously safely directed away?
If there was heavy equipment or digging on your site during the remodel, a french drain system outside the house could have been crushed or destroyed by the digging or heavy equipment.  If you know
where water goes into your french drain system and where it goes to
daylight again, you could have it camera snaked by a professional
sewer cleaning company.  You could also try a poor mans trick of
filling it with the garden hose.  If it doesn't come out the other
end, you probably have a problem.
Is your water usage excessively?  If you have a leaking water main or sprinkler system, which would probably be indicated by heavy water
usage, the water could be running underground near the foundation and
causing settling or expansion.
Last you could have an actual foundation problem.  A crack in a slab or a really old foundation (think stone not concrete) could be
failing and causing some cracking.  If your foundation is visible
around the outside of the house (most older homes have some
'freeboard' concrete showing), you might be able to see a problem. 
Or if you have a crawl space you could examine the foundation in the
crawl space.  I don't think this is especially likely unless you have
a stone rubble foundation.


So those are some very general things that could cause this problem.  I'd strongly suggest investing in an hour or two of a structural engineer's time if for no other reason than to sleep better at night.  If something really foolish has been done structurally, hopefully they would notice and you could correct it before the problem becomes more serious (structure or life threatening).  I'd also consider having a drainage guy out to look at your gutter and drainage systems if they aren't in great shape.

Hope that helps.