I got a new Civic 3 weeks ago and have had various vibration and steering
wheel shake issues. All of the problems have been corrected (mostly by
swapping wheels with another car) except one.

The dealer gave me a set of four new wheels from another car which seemed
great until I rotated them and found a shake (one wheel looked like it had
an uneven mounting surface). I had them put the good pair of the new
wheels on the rear and my original rear wheels on the front.

All is great except for one thing: When the car sits for 24-48 hours,
wicked flat spots return on the front wheels (original rear wheels). I
know it's these wheels because it first happened when the dealer put these
back on. If you drive it for 40-50 miles, it will go away (actually, when
I overinflated them and it smoothed out in 4-5 miles). Let it sit for
another 24-48 and it will return. I swear I even feel a litte something
when it only sits overnight that does go away after a few miles of highway
driving.

These wheels have nearly 1200 miles on them...will this go away or should I
push for new tires?

Note that it is 15-20 degrees here in NY pretty much night and day.