Its possible that a rim in the rear, or a tire itself is bad and now put on
the front you feel it in the steering wheel, also sounds like the vehicle
wasn't road tested after the repairs

"JM" wrote in message: "I had wheel balance and tire rotation done (rear
wheels put on front).  After that the staring wheel shakes till
approximately 24MPH.  After that it does not.
I'm wondering if something wrong with the wheels, i.e. have some bent etc..
or just bad wheel balance job. Or anything else?"

I had the same problem on both a Chevy truck and a Ford Taurus.  The rims
were not bent so that was not the cause.  On the Ford, I brought the vehicle
back to where they balance them (dealership).  They put them back on the
machine and they were still balanced.  They suggested that I had a bad rim
so I challenge this idea since the vehicle did not shake before I brought it
to them to have all four wheels balanced and rotated along with other
service work.

I swapped the tires back to where they originally were and they vehicle did
not shake.  I then talked to a tire manufacture representative and he stated
that the tire may have been the culprit due to the belts shifting.  He
stated that the belts may have worn in and I was doing more harm rotating
them then leaving them where they were.  I told him that if that is the case
then the tire must be crap because I rotated them at below 5000 miles.
These were the original tires on the vehicle.  The dealership then offered
to rotate the tires again and replace one tire at a time until the problem
was solved.  They replaced two tires before solving the problem.  Both of
the replace tires went back to the manufacture for research.  They never did
tell me what they found but I have an idea the bonding between belts was
failing.

The tires could be out of balance if they did do a poor job or if you have a
belt problem.  Try having the location where you had the tires balanced and
rotated, rebalance the tires.  If that does not work place tires back where
they were before servicing to see if problem goes away.

Sarge

My experience is wheel rotation is a waste of time.  Install and run until
tire life is exhausted, then replace in axle sets.

Fronts = typically run 40,000 under good conditions
Rear = 80,000

Less if high speed or hard driving, improper inflation, etc.

Some cars wear out the rears fast due to uncorrectable camber misalignment.
If your wheels aren't vertical to the road, they wear out faster on the
edges.

You will notice that with varying loads, camber changes to negative values.
This is due to improper design.  Camber should be unvarying with load.  In
fact, with a constant load, camber varies positive and negative dynamically
with road undulations!!  Obviously suspension engineers need to hold their
heads in shame.  They should either learn to do suspension or quit autos
and take a job with American Standard.