It could be that the thermostat has been bumped or moved. If the screws that hold it on the wall have come a bit loose when you adjust the stat it may not be straight. Causing the heat to come on when the temperature changes. As the AC runs the bi-metal strip in the thermostat will move to a point that the mercury switch controlling the AC portion will turn off the AC when the temperature reaches set point. In older thermostats like yours that also control your heating, there is a mercury switch that controls the heating portion and in some thermostats they move along with the cooling mercury switch. It may be the heating portion is triggering when the temperature starts to lower in your house.
There is also a differential setting between the heating and cooling portion that may be the problem in the stat.
You may want to change the stat to a newer digital model. With digital models you will not have this problem.