I don't know that this fits the particulars of your problem, but the problems I've had with furnces/AC not shutting off or not starting in response to set point have often fallen into the following categories:
1. Old battery in the digital thermostat. (I've seen this on several units in different home...they get squirrely when the battery is low.)
2. Air infiltration in the wall the thermostat was mounted on--had this happen last year. In this case there was an open channel up the wall to the attic. This was creating an offset in both summer and winter, most noticeable in winter when the displayed temp seemed to lag other measurements in the home...and the furnace would continue running well after the home was warm--to the point of becoming hot. I noticed the wall near the thermostat was very cold during a ~0 F night. The next day I checked the attic and found a gap in the insulation. After stuffing the cavity the unit has behaved predictably.
3. Stuck or defective contactors on outside units. Sometimes a sharp rap on the box will get them functioning (at least temporarily.) Other times I've had to replace them.