In my experience the old mercury trip thermostats with the bi-metallic strip are wildly inaccurate. My experience was similar to yours, I had to crank the thermostat down as low as it could go to get the furnace to turn off and crank it high to get it to turn on.
I'd recommend going to the local hardware store and picking out an inexpensive digital thermostat. Here is a link to a good example. It doesn't have a ton of features but it will get you the accuracy you're looking for. They're pretty easy to install, only a few wires to hookup (2 for your furnace and 3 for central AC if I remember correctly).
I've installed a similar thermostat in every place I've lived in if a mercury trip thermometer was in place ... even rented apartments.
There may be a problem with your furnace but this is a good first step to take and even if it doesn't solve the problem it's a good investment for your place. Easy to read, easy to change and very convenient.
Your furnace is shutting down on limit. There can be a number of causes for this.
Start by making sure you have a clean filter in the furnace. A dirty or restrictive filter can cause this issue. Alternatively you could also have a dirty or plugged up A/C evaporator coil which is located above your furnace. This can also cause a furnace to cycle off on high limit, however is uncommon unless you have run your furnace without a filter for prolonged periods of time. Also if you have a high efficiency furnace, there is more of a chance to have the secondary heat exchanger plug up rather than the A/C coil.
You can also have a blower motor issue. The motor can be faulty or seizing up causing it to not spin fast enough to move enough air through the furnace. Another cause may be that you have a faulty limit that is opening prematurely.
The major issue that can cause this problem is a heat exchanger issue. If your furnace is cycling off on high limit, and everything checks out, you may have an internal blockage of the heat exchanger. If this is the case either the heat exchanger or the furnace will need to be replaced. A combustion analysis of the furnace is required to prove this is the issue.
If you happen to have a 2 stage high efficiency furnace you could have a bad ventor motor gasket which is allowing air to be drawn in behind the motor. Big cracks in the condensate collector pan can also cause this but is very uncommon. You can also have the a two stage gas valve high fire solenoid stuck open, but this is also very uncommon and can only happen on 2 stage furnaces. Also if you have a bryant, payne, or carrier high efficiency, you could have a cold spot baffle leakage that is allowing air to be drawn in between the primary and secondary heat exchanger however this is also very uncommon.
If you think your blower is not spinning fast enough you may also have a bad blower motor, or if an ecm motor, the control board may be bad. If its a fixed speed motor and your getting power to it but its not spinning fast enough it could possibly be a bad blower motor. If you decide to change out the blower motor, make sure to get the appropriate replacement capacitor to go with it. I actually did have the same issue on an older carrier high efficiency furnace a few weeks back. It ended up being a bad blower motor, however the motor spun freely and had no indications of seizing or hard starting.
Best Answer
Probably. You'd have to inquire of the furnace maker if it is or is not. Speculating, since we have no information about what make or model furnace you have, it probably runs the burner until the heat exchanger is too hot, shuts off the burner until it's too cold, and starts it again. Very few furnaces have any ability to modulate the flame, so it's either on or off. In all likelihood the on/off time varies with the return air temperature (and thus, the heat load.)
The post-burn run to cool the heat exchanger after the call for heat is satisfied is certainly standard.